South England and Wales?

www.nationaltrust.org.uk and www.english-heritage.org.uk are two sites with a lot of visual info on sites and scenic walks. Too bad you don't like castles...Wales has some of the best...very historical and not too touristy. The Cornish coast is famous for seaside villages...very popular, probably need to book starting now. Look for refundable just in case. Bath is worth a visit. I personally would go back to Wales....it seems magical somehow.

I'm less sure about Wales because I have only day-tripped there (from Bristol and Chester), but Cornwall is not a place where you can just show up in the middle of the summer and expect to find a room. Having a car will help a lot, but accommodations are tight, so you're smart to be thinking about this possibility now. And if you want to have dinner sitting down at a restaurant table (as opposed to eating fish and chips on a sidewalk bench as you fend off the seagulls), you need to make a reservation. This holds true in the Cornish coastal towns, at least, and not just at fancy restaurants.

For small villages you can’t do much better than Cornwall. Using the M4 motorway as a guide, you’d have no trouble filling 10 days staying south of it. For what you said you like to do, I’d head to Cornwall.

On the other hand, we loved Wales; Tintern and its abbey, Tenby, Saint Davids, Anglesey, The whole Pembrokshire coast and the Pontcysyllte Aqueduct are great. As already stated, a main draw to Wales are its castles. For historic sites in Wales, visit CADW.

There are Neolithic sites, other than Stonehenge, in both countries if you enjoy them.

Well there is absolutely nothing wrong with either of those directions - they are both lovely and just different. With 10 days and a car, you could see a bit of Cornwall and Devon. Sounds wonderful. But like acraven said, it’s a good time to be making the decision. :)

Please don’t get off a long transatlantic flight and hire a car then head onto the busiest roads in Europe when jet lagged and driving on the wrong side of the road. There isn’t anything at Stonehenge, so are you staying in Salisbury?

Late July means it’s peak school holidays, so for this reason, I would avoid Devon and Cornwall unless you want to sit in nose to tail traffic for hours. Avoid The Cotswolds for the same reason.

Wells is charming and from here, you could walk Cheddar Gorge, climb Glastonbury Tor and visit the Fleet Air Arm Museum in Yeovilton in addition to several good National Trust properties.

You could easily fill a couple of days in Bath, then head to Wales. Cardiff can also occupy you for a couple of days and the Big Pit Museum (go down a former coal mine) about half an hour away in Blaenavon is fascinating. You have the option of heading to the Brecon Beacons, the pretty Gower peninsula or loop back round to the ruins of Tintern Abbey/Chepstow/Monmouth to explore the English/Welsh border.

Look at overseas membership of the National Trust, which will give you many options for historical days out.

We did a four week drive tour of S. Wales and England in 2017 and loved it.

Here is my detailed review with tours and hotels (B&Bs) mentioned.
28 days in Britain and Celebrity Eclipse home

https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

Cornwall would eat up several days of your time and it a always loaded with tourists in Summer. We passed on Cornwall for our trip and plan to spend a week there later.

We picked up our rental car at heathrow after our transatlantic flight and drove it to Bath (about a 2.5 hour drive). Some advise against driving after such a flight. I have done it before more than once and handled it well. I am always very wide awake and careful. Just don't plan a lengthy drive on that day.

Tips, on our tour in 2017, we only drove more than two hours on three days. Try to plan your trip so you only spend about two hours a day.

For S. Wales, we visited Tintern Abbey on our way to Cardiff and more. Many castles in Wales. Don't miss the Museum of Welsh Life just west of Cardiff. Also, consider Tenby and St. David's.

Also, we loved the Cotswolds, staying in Chipping Campden at the Volunteer Inn and used it as a base to visit the Cotswolds, Oxford, Stratford Upon Avon and Blenheim Palace.

Recommend renting a car with automatic transmission is not used to driving on the left. It costs more, but while driving on the left, you don't want to be distracted by having to shift gears with your left hand.

Make sure you rent a vehicle that has a navigation system or you have goggle maps on your cell (and cell works in the UK).

The last week of July is when the school holidays start and the roads to the scenic areas are packed and accommodation ‘tight’. The A303 which passes Stonehenge continues westward to Devon but it is not even dualled for much of this route.

Also consider the Dorset coast - especially Lulworth Cove & nearby Durdle Dor - which can be done as a day trip from Salisbury (which is just south of Stonehenge).https://www.visit-dorset.com
https://lulworth.com/visit/places-to-visit/lulworth-cove/

Do visit Bath and if staying in Salisbury consider going by train - www.nationalrail.co.uk

As others have said, the end of July is the start of the short (in American terms) UK summer school holidays. So make sure you check if accommodation is available at the places where you think you might want to go before you spend a lot of time researching places to sightsee. Most English folk reserve their summer holidays 9-12 months in advance so there may not be a ton available at this point.

Oh my I would not attempt to go to Cornwall in July and August... it is absolutely rammed!

Our family loves southwest Wales, the Solva/St. David's area is just gorgeous. And the costal path covers the length of the Pembrokeshire coastline which is fabulous... amazing walks and views. St. David's is small, charming and has great historical significance with it's cathedral. Pembrokeshire is a great alternative to Cornwall.

Good luck!