3 weeks in England

I think an RS Guide book will serve you well at this point, answering most of your questions. It's a bit difficult to suggest three week itineraries for folks one doesn't know. In addition, there are great resources here on the Forum-

Review the posts under England.
Review Trip Reports.
Review the RS suggested route in the Guidebook.
Reviews the route RS uses in his tour.
Check the related articles on the "Watch, Read, Listen" section here.
Check out Cameron's Blogs.
Join local Facebook groups which are especially good for real- time info.
Stay updated on rail strikes.

Once you've done some homework, and narrowed your interests, we can best help with specific questions.

Have a wonderful trip.

I also think it's worth talking to your friends who've already visited England. What makes their eyes light up? If the Cotswolds, Bath and maybe the Jurassic Coast makes *your * eyes light up, then focus on London plus those two or three places - that honestly sounds like plenty to really enjoy the country, and not spend it moving from place to place. Also, unless some/all of you are highly skilled drivers, decide now to skip the rental car and plan to travel by train/bus. They have a great system. This early decision will also help you plan your stops and route.

Need to rent a car to see the Cotswolds.
We stayed at the Volunteer Inn at Chipping Campden, it was nice.

Bath, we stayed at the Brooks Guesthouse and had seafood at the Scallop Shell.

Don't miss Stratford up Avon.

No trains in the Cotswolds. Personally, I think that driving is more trouble than it's worth. f you want to avoid driving, where village roads can be very narrow and sometimes bordered by stone walls, you can always take a mini-bus tour (people here seem to like Mad Max), or, as we did, hire a knowledgeable driver/guide with a big, comfortable car. Then the parking is his problem, you can pick and choose which villages you want to see, go in the opposite direction of the traffic and crowds, and stay as long as you want. We found the Jurassic Coast dull, chilly and breezy, even in the summer, and you'd need a car there. It is pretty, though, and if you're big into dinosaurs, that's the place to go. If you prefer city activities, going there might be a waste of time. Check out jurassiccoast.org. What are your constraints for lodging in London? Cost, location, nearby restaurants? If hiking about town is out, I'd suggest prioritizing your must-see sites and base yourselves there. Taxis are expensive, but you are correct in that with party of four, the cost is often reasonable. The tube is well-signed (hard to get lost in), fun and cheap, too. (Lots of stairs, though, if knees and endurance are an issue.) I don't want to complicate the issue, but maybe do some more research. Three weeks isn't a lot of time. A week in London is a good start. Pick two or three others, and spend serious time there. Bath, from which you can do a couple of longish day trips to the Cotswolds, and York are both worthwhile. Keep in mind though, while train service is good, you don't want to spend lots of time getting from place to place. York is 2.5 hours from London and might be too far out of the way. The basic RS England/London guide/s will help you a lot with your broadest of questions. In addition, try the facebook pages, trip reports etc mentioned above. All of these will help a lot, too.

We found the Jurassic Coast dull, chilly and breezy, even in the summer, and you'd need a car there.

And therein lies the issue with planning and the British climate. I've been visiting the Jurassic Coast during the summer and it's been glorious weather but I have the luxury of living close by and being able to decide whether to make the trip at the very last minute.

You also don't need a car, there's a dedicated bus service: www.firstbus.co.uk/adventures-bus/services/jurassic-coaster

And, like almost all bus services in the UK, single journey fares remain capped at £2 each on the Jurassic coaster.

Also in the Cotswolds, bus services have been substantially improved. Partly because Pulhams (the main operator in the area) are now part of the much larger Oxford Bus Company and partly because the County Council have been funding enhanced services.

Anybody who hasn't looked in the last 12 months is simply not up to date.

It is very much possible to get around the Cotswolds by public transport, and there is also (very) new integrated ticketing.

The buses are timetabled to connect with the trains at Moreton-in-Marsh railway station.

Keep in mind though, while train service is good, you don't want to spend lots of time getting from place to place. York is 2.5 hours from London and might be too far out of the way.

Several 2.5 hr train trips over three weeks is not at all unreasonable. We did Bath, Oxford, Edinburgh, York and London over two weeks and it was fine.

Edited to add: Especially when some are suggesting that the OP not drive.

Nor is York 2 1/2 hours from London- it can be 1:45. more usually 1:52.

Stay in Bath for at least 4 nights. You can explore the Cotswolds using a local guide or small group tour company such as MadMax. Many local companies provide more bespoke tours, so research online and find one that fits your needs. Bath is easy to walk around, but does have Uber if you need a short ride within the city. Some companies to check out

https://www.cotswoldsguidedtours.co.uk/. (I think they are already sold out for this September)
https://www.bestcotswoldtours.co.uk/. (friends took a two-day tour with Mark, and had a fantastic time)

I would suggest you book a private driver to Bath from Heathrow. Put London on the last leg of your trip. You can easily get to London Heathrow using the Elizabeth Line for your flight home. No need for a transit pass, just tap in and out using your US credit card. (Each person will need their own).

I never expected to visit Torquay, but some other plans fell through.

Man, it's nice in Torquay. Very Mediterranean in feel. A great place to kick back and relax.

Anybody in Torquay would be well advised to go to Paignton and take the steam railway (or bus) to Kingswear and then the ferry over to Dartmouth. https://www.dartmouthrailriver.co.uk