Stratford upon Avon and Castle Combe

I would definitely say to stay overnight in Stratford-upon-Avon if you want enough time to visit the main locations. There's a hop-on hop-off bus that takes you to Shakespeare's birthplace, Anne Hathaway's cottage, Mary Arden's farm, etc.

https://city-sightseeing.com/en/100/stratford-upon-avon/262/hop-on-hop-off-stratford-upon-avon

The bus can run behind schedule because of traffic, and once you've hopped off you have to wait (of course) for the next bus before you can continue to the next destination. So it does take a full day (or more!) to see everything.

We stayed at a hotel within easy walking distance of the bus hub; also an easy walk to the Royal Shakespeare Theatre. It has changed hands, so I can't vouch for how good it is now, but if you search by map near the Visitor Information Centre on Bridge St. and Bridgefoot Car Park you should be able to see the options.

The whole town is very much geared to tourists, meaning both good and bad. For instance, we ate at a pub called the Pen and Quill which looked really cute and advertised the best steak in England or something to that effect. We wouldn't have ordered steak ordinarily, but decided to try it. Well, it was mediocre by our standards. But the location was convenient, so can't really complain.

I've been to Castle Combe a number of times as part of either a RS tour or as part of a day tour from Bath. It's a cute village but honestly you'll spend a good bit of time getting there for maybe an hour at most of walking around. IF you were going to be in Bath and were going to do a Mad Max tour I'd say yes as this is included, otherwise, I'd save it for your next trip.

In Stratford Upon Avon we stayed at The Arden hotel. We liked the hotel and its location. We did have a rental car.

Castle Combe has recently appeared on everyone's tick list. It is pretty, but then so are many other villages in England. If you do decide to visit, it is best done from London - train from Paddington to Chippenham (about 70 minutes) and then the Number 95 bus (about 30 minutes) BUT be warned the bus service is two hourly, so check times carefully as you don't want to be stranded there!

I agree with Pam. Last year I did a Mad Max tour out of Bath that included Castle Combe. I think we had 45-60 minutes there and it was plenty of time. I wouldn’t spend a long time traveling there on my own when the town can be seen sufficiently in such a short time.

If you want to see Castle Combe, I would suggest you stay in Bath a night or two and do the Mad Max tour which goes there.
Castle Combe is close to Bath.

Castle Combe is NOT close to Stratford-upon-Avon. The distance between the two is 62.6 miles, and a car/taxi/Uber/limo journey from one to the other would take one hour and 33 minutes, one way.

I would not try to go from one to the other since you will not have a car. There are no bus routes between the two.

I recommend you stay in Stratford-Upon-Avon for two to three nights. The reason for this is (A) you will want to do all the activities mentioned by epitd (above) on the first full day there. And (B) you may wish do a tour of the Cotswolds on the second full day you are there. I recommend tours by this company:
Go Cotswolds, based in Stratford-Upon-Avon. They do a great tour to several lovely Cotswolds villages which are just as lovely as Castle Combe. They will pick you up at your hotel for the tour to begin early in the morning.
https://www.gocotswolds.co.uk/product/cotswolds-in-a-day/

When you leave Stratford-Upon-Avon, I would recommend spending a night or two in Oxford. Yes, it is worth it.

If your schedule allows, then go to Bath and spend a night or two. You can at this time take the Mad Max tour to Castle Combe and see that.
There's lots to see in Bath (start with Bath Abbey and the Roman Baths).
Great restaurants, lovely streets to stroll, and great hotels.

My husband and I loved these places and found it was well worth the time taken away from London in our itinerary to visit. We are seniors and find that, as wonderful as London is, we enjoy the slower pace of the towns named above.

Here are bus routes for the Cotwolds, in case you want to do one or two rides to explore.
https://www.pulhamscoaches.com/bus/

As you can see, no direct routes from Stratford-Upon-Avon to Castle Combe.
I don't think you could even piece it together.

If you want to go to Castle Combe from London, you can take the train from London Paddington to Chippenham, then take taxi to Castle Combe (5 miles), after you visit Castle Combe take taxi to Lacock (8miles), some of Downton Abbey and other movies and tv show have filmed there. After Lacock take taxi back to Chippenham (4 miles) to get train back to London.

Lacock was a great little town.

Last fall I spent a month in England. I visited both Oxford and Castle Coombe and really enjoyed both. I would suggest making either Oxford or Stratford a base and taking Go Cotswolds day tour which leaves from Stratford and visits several wonderful Cotswold villages. If you really want to see Castle Coombe that is at the other end of the Cotswolds and as others have stated best visited from Bath. I took the Mad Max day tour from Bath and visited Stonehenge, Avebury, Lacock & Castle Coombe. In Oxford I stayed at Christ Church College which was a wonderful way to really feel like you are part of the city. Have you been to Blenheim Palace. That is also near Oxford and a fabulous palace to visit.

I liked Castle Combe. Did it from Stratford, but I was driving and saw several other places. I agree about the hop on hop off bus in Stratford. It’s a good way to see everything