Bristol or Bath

Bath would be my ideal choice of base kressmess5 to eliminate the long bus days. Salisbury England is another option too. It is the closest to Stonehenge, less then 30 minutes away. Salisbury to have a busy rail line.

If you want to do a tour, then Bath for sure. I've done the MadMax tour of Stonehenge and Avebury from there. There are also tours either thru them or Lion Tours to Wells and Glastonbury.

You CAN do Stonehenge on your own from Salisbury. I don't know how much time you have but consider 2 nights in Salisbury so you have a full day. In the AM of the full day get the shuttle that runs from either the train station or a spot in the City Center. It's run by the local bus company the Salisbury Reds and is called the Stonehenge Tour but really, it's not a tour. They do a loop all day out to the stones, then back by Old Sarum and to the City Center again. You can purchase your ticket from the driver and get the one that includes the admission ticket to Stonehenge. He will hop off the bus, buy the tickets at the kiosk in the parking lot and off you go to pick up your audio set, have a quick comfort stop and take the small land train out to the stones themselves. Walk back to the Visitor Center via the path to Barrows and Cursus. End the day back in Salisbury by going to Evensong at Salisbury Cathedral.

https://www.english-heritage.org.uk/visit/places/stonehenge/
https://www.thestonehengetour.info/
https://en.wikipedia.org/wiki/Stonehenge_Cursus

It really depends on what you are looking for. Bristol is much larger, but is not best known as a tourist destination. Bath has the touristy places, so has more well-known attractions within a smaller area, and the sort of places which appeal to tourists - as well as large numbers of day visitors. You won't find the small quaint B & Bs and fancy tea-rooms in Bristol that there are in Bath. but there are more good-standard hotels, a wide range of specialist restaurants, etc.

Most trains from London to Bristol go via Bath - twice an hour - but Bath is 15 minutes closer. It's the same with trains to Salisbury. There are more frequent coaches from Heathrow to Bristol than there are are from Heathrow to Bath, and similarly more and faster buses to Wells and Glastonbury from Bristol than from Bath. Transport links to the south-west, midlands and the north are all better from Bristol, while escorted day trips to Stonehenge and the Cotswolds are better from Bath, since they are aimed at tourists.

If you want to see the famous sites of Bath - the Roman baths, Royal Crescent, Pulteney Bridge - then certainly stay in Bath. If you are more of a lone traveller and want to find interestingly places for yourself, Bristol has its advantages, and there are certainly plenty of interesting places too see
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As you're evaluating train options, note that Bristol has two main train stations, Parkway and Temple Meads. Temple Meads is the one you want; Parkway is several miles outside of town, with not much going on in the immediate area.

If you're set on doing a tour, rather than going by bus on your own, it'll be slightly more convenient to stay wherever the tour leaves from (usually Bath, I think?) But it's so easy to get between Bristol and Bath by train that it's certainly possible to stay in one and take tours from the other.

Bristol is a sizable city, and its local public transportation is not that great. So if you stay there, be sure to pick someplace not too far from the train station. There are many hotels in that area, although I can't advise you much on specific places since I've never stayed in any of them.

Temple Meads Station in Bristol is a bit isolated from the center of town. I stayed very near the station in 2017 and had difficulty finding somewhere to have dinner. (Do not even think of eating at the Ibis hotel near Temple Meads.)

I think most American visitors would find Bath a more attractive place to stay--and heaven knows, I'm not a big fan of Bath's all-Georgian-all-the-time architecture. I did find Bristol a convenient base for day-trips to Cardiff (by train) and Wells (by bus), in addition to Bath (also by train).

Temple Meads Station in Bristol is a bit isolated from the center of town. I stayed very near the station in 2017 and had difficulty finding somewhere to have dinner.

That's a good point - the immediate area around the station is dominated by workaday office blocks and other not very interesting things. If you want to be in a more bustling, tourist-friendly area, I'd suggest something in the vicinity of either the Bristol Marriott Royal or the Mercure Bristol Grand. (Again, I know nothing about what it's like to stay in either of those properties - I'm just going by location.) Both are a 15-20 minute walk from the train station.

Hello from Wisconsin,
Both cities are grand historic places. Bath is best known for it Roman baths. But Bristol...if you start reading English history, at some point every story line passes through Bristol. Who knew how important and big this city was in English history starting early on.

wayne iNWI

We did the MadMax bus tour from Bath and found it really fun--super easy from Bath, and a good tour of Stonehenge, the Cotswold cottages, and Avebury. The driver was really knowlegable and friendly--he was also a stonemason--and we really enjoyed hearing what he had to say.

Bath would be my choice between the two, without a doubt.

You said you are "Arriving late at night in Heathrow. "
We took the bus from Heathrow bus terminal to Bath. Just follow the signs in Heathrow to the bus (coach) terminal. Buy tickets at the window. Wait outside the double sliding glass doors for your bus.
There is no train that goes directly from Heathrow to Bath. And it may not be worth traveling all the way into London to go to a rail station for the train. We took the bus to Bath from Heathrow when we needed to be there to begin our Rick Steves England tour.

The bus arrives in Bath downtown, at the bus and train station. From there it is an easy walk into the center of Bath.
I recommend The Abbey Hotel, which basically backs up to Bath Abbey.
The Mad Max tours leave from out in front of this hotel.
Is that who you are planning to do your Wells and Glastonbury tour with?
Mad Max also does very good tours of the Cotswolds, if you are interested.

I don't know how much time you have planned for your entire vacation, or how much time you plan to spend in London. But Pam's suggestion of going to Salisbury is a good one. Salisbury is a great town, with a grand cathedral and several good museums. Also easy day trip out to Stonehenge. There are several good hotels in Salisbury, one was built in the 1400's. Interesting buildings (some medieval or Tudor) to walk around and see, too.
I would consider spending two nights in Bath and two nights in Salisbury, if your schedule will allow for that.
Salisbury is a very short train ride from Bath.
From Salisbury or Bath--easy train trip into London.

When we travel, we don't mind moving to a new place, such as from Bath to Salisbury, instead of sticking to one base. It gives us a chance to take more than a quick look at each town. Places such as Bath and Salisbury can be more interesting than London, or just as interesting; a slower pace, not as much traffic, seeing the countryside of England, meadows with sheep grazing, cathedrals, a lazy river with ducks and swans on it.