Where to live in UK for several years?

I think you will find the following You Tube videos of interest as they are made by someone from Texas who has a holiday home in Cheltenham.https://www.youtube.com/c/MagentaOtterTravels

I would rule out the north and especially the east coast due to the weather being worse. The south and west of Britain has a better climate rarely going below freezing in winter or too hot in summer. However, even in the south west there are areas to avoid due to the weather - notably the uplands of Dartmoor and Exmoor as well as exposed places on the coasts.

Exeter is a pleasant small city with relatively good weather being in the lee of Dartmoor. It also has very good rail links for getting about. Exeter airport is just east of the city but choice of flights in rather limited. Unfortunately the city centre, is a bit of a hike up a hill from the main station - St. David’s - though trains do link with the Central station.

Bristol is another possibility but the main station - Temple Meads - is a bit of a walk from the main shopping areas - one of which is rather dated (Broadmead). The city also has notorious traffic problems on all roads in/out. Bristol does have an airport with a very good selection of flights. Unfortunately it developed from a war time airfield and is not linked directly to the motorways or railways.

Cheltenham is another possibility being on the doorstep of the northern Cotswolds with bus links. Cheltenham only has a small train station but has an excellent choice of services with fast trains going north to Birmingham and beyond as well as east to London, SW to Bristol and beyond and another line to Chepstow and into south Wales to Cardiff. Downside of Cheltenham - miles from the coast.

You might also like to check out the Welsh capital - Cardiff. Excellent rail connections long distance plus the recent addition of an electric Metro network of local services. Cardiff Central station is right in the centre of the city and the main shopping streets form a large area where traffic is banned. Here you will find modern malls and older arcades with unique shops. The waterfront - known as ‘The Bay’ has also seen much redevelopment and is well worth checking out. If considering property purchase, take a train to Lisvane in north Cardiff where you will find houses with gardens. (If doing this - be sure to visit Cefn--Onn-Park which is 5 minutes from Lisvane station. Good country style pub just left of entrance for meal). The weather in Cardiff is relatively good being sheltered from the north by mountains and from the westerly winds by hills. Coast is nearby with frequent trains taking 30 minutes to reach the sandy beach at Barry Island - though this place is rather downmarket. Lovely isolated beaches are 20 miles SW of Cardiff but you really need a car to reach them. Brecon Beacons National Park is a 40 minute drive N of the city - though a bus route does exist. Cardiff has an airport but the number of flights does not come near the number offered from Bristol.

are you aware of the husband needing "Right of Abode"?

Firstly unlike James I would not rule out the north because of the weather - he makes it sound like we're close to the Arctic circle. Equally you can't rule out the east of the country entirely. It is a lot drier on the east and will also be warmer than the west in Summer (and conversely a bit cooler in the summer).
London might be an obvious choice - it is warmer and drier and of course is the best spot for airport access. But it's very large so people end up spending most of their time in the particular location that they live in as it takes a long time to cross the city. And of course it's hugely more expensive for property. The south east in general is very congested so slow to get around and less immediate access to green space. But the number one spot for train travel around the country.
James has covered many south west options.

If airport access with flights across Europe is important then really the areas around Birmingham and Manchester are the next best options after London. Both will be cheaper to live in and have airports with a lot of flight choice, although Birmingham would probably need at least a one stop for flights back to the US - Manchester is better in that respect.

I'm guessing that neither city will be on many others' lists but both would work for you if you want city life. To get a truly urban lifestyle then Manchester is these days better as it has a very large central population although they will nearly all be younger than you!
There are a huge number of smaller places that will give you a city life vibe and I will let others make their suggestions. But you are going to have to make some compromises on your brief to find what you want. Single storey housing with garden space is not widespread and will be virtually non-existent close to any city and trying to match that with a desire not to have a car will make the search very, very difficult.

And of course make sure that you sort your residency out.

I’d actually recommend Bath. I think you’d like the small city vibe, it’s a quick train ride to London, has all amenities you’d need without feeling like a very gritty, urban environment. Bristol airport is a taxi ride away with good links to most of Europe.

If you wanted a larger city then Bristol has a lot to offer with some lovely areas but it’s not all pretty like Bath. Public transport is patchy and the traffic is terrible.

There are very few bungalows available in most cities but if you wanted to avoid stairs you could get a ‘garden flat’ which is the ground floor flat usually of a converted Victorian house which owns the back and sometimes also front garden. Most purpose built flats do not have private gardens.

If you were thinking East Coast then East Anglia- the northern part of Essex, Suffolk or Cambridgeshire could be a very good idea. For easy access to Luton and Stansted airports for the low cost carriers, and very easy access to London.

East Anglia in particular has a very equable climate.

But even in Northumbria it really isn't anything like the Arctic as implied elsewhere. Particularly in the South of the County (south of Alnwick) there is easy access to Newcastle (to become even easier in a week or so when the Blyth and Tyne rail line re-opens). In fact the county usually escapes the heat of summer and more often than not escapes the winter weather unless we get a system in from Siberia- not that often it happens.

Anywhere you go to in the UK there are always lots of opportunities for volunteering.

The significant challenge is going to be in finding bungalows (single-level homes).

I live on the edge of the Lake District but am only 3 hours (2 by car) from Manchester, Newcastle, Liverpool, Glasgow and Edinburgh Airports- journeys the locals do all the time and don't give a second thought about.
Likewise we just go the cities for the culture, don't even think about it and stay in budget hotels like PI's. But we have our own culture as well- a number of theatres, movie theatres, music societies. You would be surprised what there is in the area. And the Lake District Music Festival each summer which brings world class music and musicians to the area.
Being on the edge of the area I don't suffer locally from the over tourism of the Central Lakes. But have abundant access to hiking and biking routes (am on 3 cycle routes). My own street actually has Bungalows with gardens, we have loads of volunteering options in town and in fact 2 gardening clubs within a 5 minute walk of where I live. Last year I put down salt on 2 days over the winter!! I am not at all promoting my area to you, just saying there are many places where you can be in the countryside but also get easy access to the city.
The Peak District being another such example- for Manchester, Sheffield and Derby. Except for a lack of bungalows my birth village of Gee Cross (just outside Hyde) on the very edge of Manchester, historically in Cheshire and almost on the edge of the Peak District would be a good place for you.
Or the Wirral (the Cheshire part of 'Merseyside') for Liverpool and Chester another which would fit all your criteria. The Wirral has a number of lovely what you could call urban villages eg Hoylake (hands up, almost 100 years of personal family history), Bebington or Bromborough just as examples. Liverpool is just across the Mersey but all three are nice distinct communities.

Adding to some of the points above. Re access to airports, I know from relatives in the North West - in what is the Fylde area - that there are a lot of local reasonably priced car services/drivers to nearby airports (Manchester in particular). As well as whatever public transport is available. I'm sure its the same in many other locations.

Another thing to play around with, to get an idea of what is available to rent and at what price. Look at www.rightmove.co.uk.

What about Oxford? This is just one of several exploratory visits, yes? Oxford offers a number of cultural activities - you can stay in the suburbs but have easy access into town. Plus easy access by bus to LHR for travel.

You get much better value for money in terms of housing the further north you go. Greater London and south east England are good if your budget is unlimited. Where is your wife from originally? That would be a logical place to start looking maybe.

I'd probably vote for having a looking at the central belt of Scotland. There's many pretty places to stay that are within easy reach of Glasgow and Edinburgh, but still remain rural.

If your interests are outdoorsy, I'd probably still want to own my own car. It opens up a lot of the country that's just out of reach with public transport. The UK's probably still one of the cheapest places to buy and run a small car in northern Europe. There's a huge surplus of used cars which keeps prices down compared to other countries. You get six months of driving on a licence from a US state before you have to take a UK test I believe.

I agree that starting where your wife is from would be a good idea- as she will have roots and local knowledge (even if it is some or even many years old) that would help you to assimilate into the local area and local way of life- begin to make connections if you like.

And the Central Belt of Scotland does not normally get severe winter weather- that comes further north. Also you avoid the midges of summer, who are a Highland beastie.

In the Edinburgh area there are lovely parts of East Lothian and the Scottish Borders which give all the benefits of country living and access to big city life. Fife (across the Forth Bridge) would be on the search list (away from the tourist hotspot of St Andrews).

And head west from Glasgow into either Inverclyde or Dunbartonshire you leave the city behind incredibly quickly. I've never really thought about it before but there is probably much more traditional single level housing out there than you would find in a typical English area. That is far more Gerry's part of the world than mine, but that is the gut feeling I get from quite extensive travelling in the area.
If I was choosing my last home to be in Scotland (and I have thought seriously about it) I would choose Orkney or Shetland (strongly tending to Shetland) or one of the Clyde Islands but that is me- the antithesis of your wish list. Those far north islands may be windy and cold but they don't generally get the extremes of winter either as the climate is too marine.

Thank you all so much for your suggestions! And weigh in, anyone else who wants to give them.

I appreciate the rental price comparison info as well as the info on used car buying.

Katy mentioned Rightmove above. Zoopla is another large real estate website, aggregating many independents.

If I were going to expand on my post, a contributor mentioned Alexandria in the west of Scotland in a post which seems to have gone. Balloch is one town worth a look. It's right on the shores of Loch Lomond as a gateway to the Highlands, but is within easy reach of Glasgow. Milngavie and Bearsden are north Glasgow suburbs with quick and easy access to some great country. I'm from Lanarkshire, but if I were to go back to Scotland I have a hankering to look at one of the Ayrshire coastal towns to live.

Nearer Edinburgh, you can look up the East Neuk of Fife for some lovely coastal villages, or East Lothian. South of Edinburgh there's places like North Berwick and Peebles heading towards the border with England.

You can plug some of these places into the property sites and see if anything takes your fancy.

A car is a bit of an undertaking so it would be up to you to weigh it up. I'd factor in working towards a UK licence as soon as landing in country. It would be foolhardy for a US driver to attempt to pass a UK test without prior professional instruction I think. Even the smallest towns have a driving school or independent driving instructor. It opens up a much greater choice of where you can live and visit though.

The best research for this project is Escape to the Country. God, I love that show!

As someone who lives in the North West, I can assure you that we can have hot weather in Summer and also short lived sub zero temperatures in Winter.
How about one of the Cheshire towns. You'll get more for your money and can be close to Manchester or Liverpool airports.
Close to the two big cities of Manchester and Liverpool.

Firstly unlike James I would not rule out the north because of the weather - he makes it sound like we're close to the Arctic circle.

I have nothing to contribute, but cracked up at the above from Johnnew52, lol! Although I am reading all this avidly. There is probably no chance of me ever being able to move to the UK, but it's still fun to dream.

East Anglia would be my recommendation. North Essex and the town of Saffron Walden has good links to Cambridge, London, and Stansted Airport. East Anglia is one of the driest areas in the UK. There are plenty of country walks and good bus routes throughout the area. My second recommendation would be Bath in the South West of England.

Also consider access to healthcare, access to private healthcare in a larger city might be your best option upon arrival. I am an ex-pat, my husband is American and I once dreamed of moving back to England, but now in my early years of retirement, I am satisfied with a few trips across the pond 2-3 times a year. Financially, it would not be beneficial for me to move back.

I also love watching Escape to the Country which is available to US audiences on Britbox.

Bath has been mentioned but note that all the houses are old, expensive and will be costly to heat. Some new well insulated houses have recently been built on the north side near Beckford’s Tower and they are served by the frequent Lansdown Park & Ride buses. (You certainly would not want to walk up those hills).