Best base (or two?) to see Bath, Stonehenge, Oxford and the best of that region

I would suggest Bath, we stayed at the Brooks Guesthouse, which is at a great location and parking is nearby.
Also, don't miss the best fish and chips in England at The Scallop Shell Restaurant.

Parking in Oxford is difficult, but there is parking at the city's edge.

Consider visiting Avebury, which has stones that you can walk up to and touch. Also, consider visiting Wells and Glastonbury.

https://www.gwr.com/your-tickets/ways-to-save/offers/great-west-way

Maybe Swindon or Didcot Parkway would fit as the mid point of the destinations you want to cover.

Maybe check if the rail rover Great Western discoverer west will work for your itinerary.

Mad Max tours in Bath would be useful. I intentionally went to Avebury instead of Stonehenge because you can walk right up to the stones at Avebury.

Although Swindon & Didcot Parkway make excellent places for exploring the region by train, that are not exactly wonderful places to stay. (Don't believe me - then go on Google Maps and zoom down to Steertview to see what they are like). Check any ‘pass’ prices against actually paying for going to places. For short trips, pay on the day returns are quite good value. The following site is for Rovers that can be bought in the UK. For Bath, Wessex region is probably the most appropriate:>http://www.railrover.org/index.html

I would suggest that Bath offers a good location for doing day trips in this part of Britain by train and is a nice place to stay. The downside would be more expensive hotels. From Bath, you can easily go by direct train to Salisbury (wonderful cathedral) and use the Stonehenge Shuttle Bus. You can also go by direct train to Cardiff (castle) from where you could take the 32 bus the 5 miles or so to St.Fagans Castle & Museum. For Oxford, you would need to change at Didcot Parkway so that is easily done. If you want the seaside - direct train from Bath every other hour to Weymouth. Bristol is just a 15 minute train ride away though I am don’t think much of the city centre. From Bristol (Temple Meads is the downtown station), trains go down to the south west.

Bath and Oxford are 70 miles - more than 2 hours apart. Swindon is about half way, but you wouldn’t want to stay there.

It would make more sense to stay in Bath for a few days then move to Oxford, as trying to cover places in between without a car isn’t easy. As far as I am aware, luckily, Uber doesn’t cover the Cotswolds area. A dreadful company.

I don’t know why Geogragriffith keeps on repeating the same post about The Scallop Shell. It’s not the best fish & chip restaurant in England nor has it ever been from what I can see!

Thanks for all the advice, and the tip about Rovers and the other ideas. We have some planning to do. Our trip is in May/June.
After seeing this part of the country and a bit of Wales, we plan to go back to London and take the Chunnel to Paris for a few days, including our anniversary. (I know everyone says it's kind of boring, but it seems like a cool thing to do.) I'll check the boards for that leg of the journey!

We have spent about two months in the UK in the past 10 years and eaten a lot of fish and chips. The Scallop Shell was by far the best. Also, everyone at the Brooks Guesthouse was raving about it as well. If there is better, I would like to know, so next time we are in the UK, we can try that restaurant.

Really the best fish and chips has strayed way off the original topic, but as it's been raised.
The "best fish and chips" will always be a subjective question. Too many variables and individual tastes. There are several places in Whitby which would challenge you on that title, as might Rick Stein in Padstow.
When I lived in Southend I had one just round the corner from me. The fish was always fresh very local fish (not frozen), it was always freshly cooked. And you could tell the difference. If I was running late coming back from work in London he'd even stay open a bit late for me if asked.
I thought that place was really good. But not the type of place that felt the need to promote itself or claim glory, just got on quietly with the day to day job.
I can't think of many fishing ports within a 5 minute drive of Bath.
Close to me in the Lake District I have several fish and chip shops which are run by Greek Orthodox owners. I'm not sure what they do with their batter, but it's really good. In Keswick many people say The Keswickian is the best in town. I'd very quietly disagree. But the Keswickian has the best location and promotes itself.
Have you ever tried it cooked in beef dripping? Not many places do that now, many people think that's the best way to do it. Try fish and chips at the Heritage Museums like Beamish or the Black Country.
Do you like skin on or skin off?
Personally I'd be sceptical if a place in a tourist hotspot like Bath was really the "best" whatever that word means.

I had fish and chips at brew pub in Manteo, Virginia, USA. After I ordered, the waitress returned.

Her: "We made a great deal at the dock on flounder this morning. Would it be okay if we used that for your fish?"

Me: "Let me make sure I understand. You want to sell me beer-battered flounder at the cod price? Oh, HELL YES."

Joyce,
Two good choices would be:

Bath for 4 nights.
There's plenty to see here; the Roman Baths and Bath Abbey would be at the top of the list.
Lots of good restaurants in Bath.
Walking tours of the city from the Tourist Information office.

Take day tours with Mad Max Tours.
They have a trip that goes to Stonehenge and the Cotswolds.

Oxford for 4 nights.
There is enough to keep you busy here without ever leaving Oxford.
Don't miss the most excellent Ashmolean Museum.
Take a walking tour of the city from the Tourist Information office, most often led by guides who are students at one of the colleges.

You can take a city bus a short distance north to see Blenheim Palace, where Winston Churchill was born. (He and his parents did not live there, but were visiting for a house party when his mother went into labor.)

From Oxford, you can easily catch a train early in the morning to Warwick and see Warwick Castle. After lunch, continue on the train to Stratford-Upon-Avon if you wish. Train back to Oxford at the end of the day.

I would suggest a third destination--well worth the effort to move hotels.
Travel from Oxford to Windsor by train or bus/coach.
Windsor for 2 nights. See Windsor Castle, walk around this lovely and interesting small town. Lots to see and do here. Take a river cruise on one of the many small boats here.
I have hotel recommendations for Windsor if you want them.
Windsor is lovely.
Well worth it to move hotels to stay here.

Windsor is very near Heathrow. Take a taxi to Heathrow for your flight home. We paid 20 pounds for the taxi Windsor to Heathrow in 2018....but it won't be that now, will be a bit higher......still, it's the best way to go.