3 nights Bath & 5 nights London, Sept/Oct, car rental ?

If you will utilize the car on the way from Heathrow to Bath it makes perfect sense to get the car at the airport. As to where to return the car, you might want to see if you will pay a penalty to drop it in Bath, and how much it is. Another consideration is if you would use it to make any stops between Bath and Heathrow.

Bath is very congested so you might find it difficult or expensive to find parking. Check whether your hotel has free parking. You might find it more convenient to find accommodation in the countryside if renting a car.

Consider taking the bus link from Heathrow to Reading and then the train to Bath. That way you will not have the risk of driving on strange roads with possible jet lag. You will then be able to look around Bath without having the hassle of a car.

You can, should you wish, take the train from Bath to Salisbury & then shuttle bus to Stonehenge - then back to Salisbury to see the medieval Cathedral before train back to Bath. http://www.english-heritage.org.uk/daysout/properties/stonehenge/
http://www.visitwiltshire.co.uk/explore/salisbury-and-surroundings

On another day, you could take the train (or drive) to Cardiff > things to see = www.cardiffcastle.com ; www.museumwales.ac.uk/cardiff .
You could also take a 17 minute bus (No 32/320 from central Cardiff but may be only hourly) ride (or M4 Junction 33 if driving) to www.museumwales.ac.uk/stfagans/ or take a 17 minute train ride north to see the huge medieval castle at Caerphilly. http://cadw.wales.gov.uk/daysout/caerphilly-castle/?lang=en
www.visitcardiff.com (Cardiff is about 1 hour by car or train from Bath). Castell Coch is found just N of Cardiff (M4 J34) http://cadw.wales.gov.uk/daysout/castell-coch/?lang=en
Cardiff Bay is also worth a look = 1 mile S of city centre - bus No 6 very 10 minutes.

I don't think much of Glastonbury though nearby Wells is worth a look but the Cathedral is not as impressive as that at Salisbury. However, if doing Glastonbury, you might like to combine it with > http://www.cheddargorge.co.uk/about/contact-us/

If hiring a car, you could easily drive from Bath to SE Wales and visit the Wye Valley which has Chepstow Castle & TIntern Abbey (ruin). You could even go down a Welsh Coal Mine at Blaenavon = about 1 hour's drive from Bath.http://cadw.wales.gov.uk/daysout/tinternabbey/?lang=enhttps:
//www.museumwales.ac.uk/2235/

The mine, could also be combined (by car) with Raglan Castle =http://cadw.wales.gov.uk/daysout/raglancastle/?lang=en
and then Tintern Abbey & Chepstow Castle before returning to Bath.

If hiring a car from Bath, try & visit the village of Castle Combe.

http://www.railair.com

It is cheaper to advance book rail tickets for the London > Bath route.http://www.firstgreatwestern.co.uk

"I'm thinking about renting a car at Heathrow and then driving to Bath. This way I we can potentially see Windsor castle on our way to Bath and also have a car to explore Stonehenge, Avebury, and Glastonbury while we are in Bath.

Does this itinerary sound reasonable?"

After getting off a transatlantic flight, driving on the other side on unfamiliar roads/signage etc, honest answer, no.

I have picked up a car upon arrival at Heathrow (flight from Seattle) but had to stop and get my bearings at the first opportunity. I would not try to add any detours or sightseeing on this day. Therefore, I would pick up the car in Bath, after a night's sleep, when you're ready to branch out. So far, in several visits to London, I have not yet prioritized Windsor Castle in my plans. But I consider Avebury a must-see and also recommend Blenheim Palace with a car.

The last time I did this, I took the train from Heathrow to Bath through Paddington. Then got a good night sleep, spent the next day seeing Bath without a car. Then when I was ready, picked up the rental car in Bath, drove around the Cotswolds, and returned the car to bath, and the train back to London for the London phase of the trip.

As was already said above, this avoids having you drive on the wrong side when you're already exhausted from the trans-Atlantic flight and jet lag.