Starting in Bath

We loved Bath and stayed two nights and moved on to the Cotswolds. After the trip I wish we had taken a few hours to see Wells Cathedral. We drove by Stonehenge and that was enough for us. Others will disagree. Oxford and Windsor are definitely worth the time. A walking tour of Oxford from the visitor center is good. We attended a Evensong service at Christ Cathedral, a highlight. Enjoy the process of planning!

Will you have a car?

If not, look into Mad Max Tours out of Bath. I can personally reccomend them. They do day trips to the Cotswalds. Stonehenge, and more.

Also check out London Walks for walking tours both in London and "Days Out" tours to places like Oxford and Cambridge. (I've done both and they were excellent.)

Plan how many days you spend in Bath by how much you want to see outside the city.

We were in Bath as part of a group tour of the UK for a few years ago in the summer. My experience with what you've listed:

Roman Baths - you can easily spend a couple of hours here especially if you have the audio guide and listen to all the options. Really fascinating though it was crowded. We also had lunch in the Pump Room above - a menu selected by the tour company but it was excellent.
Abbey - couldn't tour it as graduation ceremonies were happening in Bath that day and it was blocked off.

The same for the Assembly Rooms above the Fashion Museum but the museum was open and I spent a couple of hours there (without my husband) and it was very well done. Nice gift shop too.
Jane Austen Centre - I'm a Jane Austen fan and thought the price wasn't really worth what there was to see. It might be fun to go to the tea room or for a special event.
The Circus is just a ring of town houses unless you have a guide that tells you more about the history of how and why they were built.
You could spend a morning touring the Abbey and Roman Baths, walk to the Jane Austen center for lunch in the tea room, walk down past the circus (& the crescents) to the Fashion Museum. Bath center is easy to walk around.

Have not been to Bristol but our tour did include Stonehenge which is interesting especially now that they have personal audio guides. Our group didn't have time for the museum which looked well done. With travel time to/from Bath it's pretty much a full days experience.

Seeing the attractions of Bath itself is at least a day and a half. The first two weeks of April will be Easter school holidays, so places will be busy and more expensive.

What do you want to see in Bristol? I have been numerous times on business, but it’s not a usual tourist destination, just a regular city. It’s only 15 minutes by train, but could fill another day.

Stonehenge is between Bath and London, so can be done from either place, but is longer from London. Assuming you want to go to the visitor centre and not just drive past, it would be around 2.5 hours door to door each way by train (from Bath to Salisbury and then take the tour bus to Stonehenge). You then need at least a couple of hours there, so is going to consume most of a day. Do you want to go because you are interested or because you think you ought to go? Many posters on this forum mention that they feel they ought to go but it’s not of particular interest. Personally, it wouldn’t make my top 100 things to see in the U.K. list, but it’s your trip not mine.

The list of other places that you mention are all best covered from London.

As Jennifer says, Stonehenge will take up what amounts to a full day from Bath. You could do it by public transport (assuming the shuttle bus from Salisbury train station is running) or on a day tour such as Mad Max.

As Jennifer and others commented, if you're only including Stonehenge because you think you ought to, perhaps skip it. OTOH, there's more to see there than just the henge. The visitor centre has beautiful & informative exhibits indoors and out, there's a large book/gift shop and a very good cafeteria, and the audio guide really brings the henge and surroundings to life. Be aware that it is very exposed to the elements, so be prepared for whatever the weather might throw at you (we were lucky to have a dry, sunny day).

We will not have a car.

I am so thankful for the Mad Max tour suggestion! It looks ideal.

I don't have a strong interest in Stonehenge, but my husband does, and I am happy to see it. We live in a so called "historical district" here in the States, so by virtue of age alone, we will be impressed.

As far as Bristol goes, I was planning to take a Banksy tour, walk across the Clifton Bridge, and see the SS Britain but thanks for the feedback I'll rethink if it's worth it. I may replace that day with the Glastonbury, Wells & Cheddar Gorge Mad Max tour.
Thanks everyone!

We also took a Mad Max tour from Bath. It was a visit to Stonehenge, Avebury, and two villages on the southern fringe of the Cotswolds (Castle Coombe and one other). It took a whole day and it was worth it.

If you are hardcore on Jane Austen, check out Sally Lunn's for lunch or dinner (near the Abbey). Home of Sally Lunn's Bunns, supposedly referenced by Jane in one of her books. As I recall, she didn't actually spend much time in Bath and didn't really like it.

Avebury IMO is a much better experience than Stonehenge, where you can get up close to the stones.

Wells is one of my favourite places in England. The cathedral, Vicars Close and the Bishop’s Palace are interesting. Glastonbury on the other hand was tacky, but the walk up to the Tor was worth doing. The town of Cheddar is also tacky, but the circular walk at the top of the gorge is the best way to see it. You don’t see much just driving or walking at the bottom of the gorge.

To me 2 nights in one location is just 1 full day and some parts on either side. If you do a full day trip to Stonehenge (and Mad Max used to have one that went to Avebury as well) that is your full day. You'll not have time for Bristol or to really see Bath.

I agree with the comment upthread on the Jane Austen Centre. Really a disappointment. She didn't live there and they have nothing original of hers. Not worth the money. One year I did do a walking tour of Bath thru them and thought it was great and worthwhile.

I'd suggest #1 Royal Crescent which is a restored Georgian townhouse that is very interesting - much moreso than the JA Centre. Sorry...and I REALLLY wanted to like it!

I'd also recommend a walking tour if you can work that in. There used to be free ones by the Mayor's office but I did a paid one and it was a nice small group with a excellent guide.

If you are going to replace Bristol with Glastonbury/Wells on a Mad Max trip then that is about a full day as well. So that's 2 full days for day trips and no time for Bath itself.

And no, none of your day trips listed should go from Bath if you are using public transport.

BTW, I love Bath and have spend 3-4 nights there and still not seen everything. I know most people don't have that kind of time, though. I have done a couple of day trips using Mad Max and they are great. Small vans, knowledgeable guide/driver, efficient sightseeing and worth the price.

My partner and I have both have had a long interest in Stonehenge's history and visited several times early in the day in different lights. Many of my photographs didn't have any other people in them. The winds can be ferocious there so be prepared. Definitely use Bath for your day trip to Stonehenge as it's much too time consuming from London. We loved Mad Max's tour and found Castle Combe to be one of the most beautiful villages we found. We are into architecture, art and history so Glastonbury's Cathedral ruins were really fascinating to us. We even had a fine picnic lunch at the site. We also loved Wells Cathedral and especially the mechanical clocks there. We were watched intensely by cats perched at various places in Vicar's Close. There's so much to do in Bath and some fine food as well - don't miss the Scallop Shell. The Holburne Museum will be of interest to artists and art historians. I know Avebury is considered as significant if not more so than Stonehenge but I didn't quite enjoy the site as much even though you are among the stones. We did enjoy our time there with all the sheep but watch your step! As far as stone circles go we definitely were most fond of Castlerigg Stone Circle in dog-friendly Keswick.

I really enjoyed the Costume Museum in Bath.

"How many days should we devote to Bath and the surrounding area? Is 3 days, two nights sufficient?"
It depends upon how early you arrive on the first day you are there. Will there be enough time on that day to see some sights? Or will you be arriving in late afternoon?

I would do three nights in Bath.
On the day of arrival, you could see one or two sights.
Then spend night One in Bath.
On the next day, you could do the sights you have mentioned:
"We intend to see the Roman Baths, Abbey, Circus, Jane Austin Centre, and the Fashion Museum."
Then spend night #2 in Bath.
The next day, you could do a tour that includes Stonehenge.
This will be an all-day tour, returning you to Bath to spend that night (night #3).
Here's the tour company Frank II recommended:
https://www.madmaxtours.co.uk/all-tours
These tours depart from near the front door of The Abbey Hotel.

"I may replace that day (Bristol) with the Glastonbury, Wells & Cheddar Gorge Mad Max tour. "
Excellent decision.
Wells Cathedral is stunning and may be your favorite sight of your entire trip.

"The remainder of our trip will be to London, with the intention to have a few days trips perhaps to Windsor, Oxford, Cambridge, or/and Hampton Court Palace. Should any of those days trips happen while we’re based in Bath?"

No. These are best done from London if you are wanting only day trips.
Look at the London Walks link that Frank II gave you for their guided day trips.

You could consider traveling by train from Bath to Oxford, staying there two to three nights, then it would be an easy train journey from Oxford into London. There is certainly enough to do in Oxford to keep you busy for longer than a day trip. Good restaurants, cafes, pubs, hotels. Don't miss the excellent Ashmolean Museum there. You could see Blenheim Palace, just outside of Oxford. And of course, the walks around the colleges.

As another alternative, when you leave Bath, you could take the short train ride to Salisbury and stay there for two nights. Stonehenge is just outside of town. Take the Stonehenge Bus (round trip) from near the Tourist Information centre downtown. Salisbury Cathedral is amazing and has a copy of the Magna Carta on display. Then it would be an easy train journey from Salisbury to London.
If you planned on going to Salisbury after Bath, of course it would make the Mad Max trip to Stonehenge unnecessary, so you could substitute the Glastonbury & Wells Mad Max trip instead for that trip out of Bath.

Salisbury and Bath are two of my favorite places in England.
You will want to leave time in either one for just walking around and exploring.

You said that you will have two weeks. You definitely have time to choose a couple of places besides Bath and London for 2 to 3 night stays if you so desire.

We stayed in the Brooks Guesthouse a great B&B.

Also, don't miss the fish and chips at this great restaurant (The Scallop Shell).

We spent three nights in Bath and spend a day and a half in Bath, also did a day trip to Wells and Glastonberry.

I would not recommend using Bath to go to Stonehenge. That is too far. Better to do from London.
Sorry, why Bristol?

We did Oxford and Cambridge in single days. Better to do those on day trips from London.

Why not a day or two in the Cotswolds, we stayed in Chipping Campden.
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

Thanks everyone for the suggestions!

Based on your suggestions we will spend a leisurely afternoon/evening in Bath when we arrive, walking around exploring as Rebecca mentioned. Then plan to take the Stonehenge, Cotswold villages and Avebury tour the next day, spend the middle day in Bath seeing the sights, followed by the Glastonbury, Wells & Cheddar Gorge. It arrives back to Bath around 5:30 PM. So one final evening to have a good meal, perhaps at the recommended Scallop Shell, and then head to London in the morning.

Great! So 4 nights in Bath is about what I would enjoy!

BTW, it's been a few years but I enjoyed a delicious meal at Yak Yeti Yak Nepalese restaurant which is near your proposed hotel!

We really enjoyed a dinner at the Giggling Squid Thai restaurant in Bath - an interesting chef, very nice staff but a bit of wait due to it's popularity. The food was exceptional and reasonably priced.