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