3 weeks this summer in the UK with 4 small kids- question 1

Of course, you know your children better than anyone else, but I'd tend to go with (1). Every time you relocate, you have a new set of adjustments, not to mention the work of packing & unpacking for kids who are presumably too young to be responsible for their own belongings.

A central location that's not too touristy could be Cambridge. That would put you in range for Stratford-upon-Avon as a day trip, also Warwick Castle (appealing to kids), and Sandringham in a different direction. You could take the train into London for a day.

If you want some beach time, tennis, rough golfing, croquet, afternoon tea, coastal walks and wonderful kid activities I can highly recommend the family friendly https://www.knollhouse.co.uk/. It really has something for all families to enjoy. We spent several nights here 2 years ago booking with half board. We thought it was reasonable in price for all that they had to offer. I’d go back for a relaxing vacation from my vacation in a heartbeat. BTW other than walking the coastal path, we traveled by frequent bus, the Purbeck Breezer, that stopped right in front of the resort.

I had to look up the Knoll House and see it is Studland, Dorset = south coast of England west of Bournemouth.

Studland Bay is a lovely area of shallow sheltered water but watch out for nudists on part of the beach. You could go by steam train from Swanage to Corfe Castle. A disadvantage of this area is that with sea to the south, you basically have one road going east to a ferry that crosses to Sandbanks on the western side of Bournemouth (which is a very seaside town). If doing that - be sure to visit Compton Acres Gardens. You could also drive west to Lulworth Cove & Durdle Dor = a spectacular bit if coast. Click this map and take a look around this area. https://www.visit-dorset.com

You probably would not want to spend all 3 weeks in one place. You might also wish to consider Cornwall?

Not sure that the kids would be interested in old buildings in Cambridge. I think a coastal location would be a safer bet.

My initial thought was that somewhere on the coast would be good too, but geography dictates anywhere coastal is not going to be a central location to explore from.

For me, you can’t beat Pembrokeshire for charm and a lack of tourists. It’s not exactly untouristy, but it’s hardly swamped even in summer.

You probably know this, but it can, and more than likely will, rain on several days and be chillier than you would like on several more. There’s a reason the British love their holidays to Spain and Greece so much. We go to Pembrokeshire for a week every August and it has always rained heavily for at least one day and been wet in some way for 1-2 more. You have to just go with it. You hopefully get some lovely weather in between.

In Summer, self catering places tend to be booked by the week, usually starting at the weekend.

If you want to get some variety I would suggest taking three separate weekly rentals in different areas. That way you only have to move twice and you get to see some different areas as well. With small children I would have at least one week by the beach.

I'll cast a vote for Northumberland. It has gorgeous scenery, not as many crowds as elsewhere, beautiful coastal towns and sandy beaches, boat rides to see dolphins and lots of birds, many castles, hiking, and it's quite easy to reach places like Edinburgh, Hadrian's Wall and York (lots of Harry Potter stuff there). https://www.visitbritain.com/en/destinations/england/northumberland

There are so many places there to explore in that area. I will be there for 6 nights this coming April, and have already found myself frustrated because I can't see it all. So I'm sure I will be back.

Personally I wouldn't choose a coastal location. In general, any place on the coast won't be convenient as a central hub for day trips, and you'll probably be surrounded by crowds of UK residents on their holidays. And, as others have pointed out, UK weather can be cold and wet even in midsummer.

There are many places all around Great Britain that fullfill your wish for "not too touristy, but full of charm and things to explore." To avoid the "too touristy" spots, I would look at the locations most talked about in this forum and most served by package tours.

Lucky you, to have 3 weeks!

Northumberland would be good. There is a lot to see that children enjoy - castles, rowing boats, Beamish museum is great. The National Trust places have good play areas. Then there’s the beaches as well, but it’s in the North so the weather can be quite cool even in summer (the local kids will be in the water with their swimsuits on regardless. They’re hardy up there).

I loved York and could see being there with children.

From mid-July through August, British schools will have their 6 weeks summer holidays, so be aware this time will be peak travel season with crowds and higher prices. Many popular destinations will already be booked (I am thinking about places such as Cornwall and Devon). With young children, I would lean towards Airbnb Vrbo, Sykes Cottages, and Cottages.com. You don't always have to rent for an entire week. Renting a car would be better outside of the cities. Perhaps arrive in London, spend a couple of nights, and train up to York. Rent a car and go into the Yorkshire Dales and Moors, or down into Whitby and Robin Hoods Bay if you want the coast. There is the North Yorkshire Moor Railway from Pickering you could take - a great steam train journey for the kids. Other scenic places are the Lake District and Peak District. I would not base myself at Cambridge. The city will be expensive for a week, a car is not a good idea here, and Warwick and Stratford are too far from Cambridge for day trips. While Cambridge is lovely, I am not sure it would be fun for young children. If your idea is to get out into the countryside, then Yorkshire is one of my favorite areas. Lots of walks, streams, ice cream, old-fashioned candy stores, fish and chips, and sheep.