Looking for suggestions for repeat trip to Bath

I'm working on the basis that you have seen the sights in central Bath, and that your transportation will allow you to go up to about 50 miles from the city. Here are some suggestions, but you will need to Google them for details.

BATH
Holburne Museum, Prior Park, American Museum, Kennet & Avon canal path, Theatre Royal (go see a play), Toppings book shop
WITHIN 20 MILES OR SO
Bristol, Castle Combe, Lacock, Bradford on Avon, Tyntesfield, Dyrham Park (if it is open), Westonbirt Arboretum, Wells, Glastonbury, Farleigh Hungerford Castle
UP TO 50 MILES OR SO
Chepstow Castle, Tintern Abbey, Caerleon Roman Fort, Cardiff Castle, Castel Coch, Berkeley Castle, Stonehenge, Avebury, Stourhead, Cotswolds area generally, Chedworth Roman Villa, Cirencester (for Corinimum Museum and the amphitheatre on the outskirts and because it's an attractive town)

That's off the top of my head, and I have probably forgotten many others

Think I'd plan to do at least two day trips (and make them all day affairs) to the Cotswold area. Stonehenge and Avebury would also be high on the list.

Wow, Bob did an excellent job. I will just add Salisbury for the within 50 miles range.

BTW, the American Museum has a shuttle van that picks up and drops off throughout the day in case you don't want to drive out there. They pull up in the Terrace Walk area where the big tour buses drop off.

Bob gave you some excellent suggestions, as did Pam and TC.

Even though you will have access to a car, you may prefer to take a tour on a small mini-bus, relax, and let someone else do the driving.

Consider Mad Max Tours.http://www.madmaxtours.co.uk/
They are a family-owned tour company based in Bath. Make a reservation online, or call them. On the morning of the tour, meet outside Abbey Hotel, 1 North Parade, Bath, and wait near the coach pick up area.

Tour Number One takes you to Stonehenge, Avebury, Lacock Village, Castle Combe Village, Silbury Hill and Cherhill White Horse.
http://www.madmaxtours.co.uk/tours/stonehenge-full-day-tour
Tour Number Two (and 2a and 2b) takes you to Cotswold villages.
http://www.madmaxtours.co.uk/flip-box-tour-2
Tour Number Four takes you to Avebury, Lacock Village, Castle Combe Village, Silbury Hill and Cherhill White Horse:http://www.madmaxtours.co.uk/tours/avebury-stone-circles-castle-combe-in-the-cotswolds-and-lacock-village-tour

Thanks everyone for your great suggestions. Prior to moving to Bath my son lived in Oxford for 6 years, so we've pretty much exhausted the Cotswold and Oxford areas as well as London, Cambridge, Harrogate (my personal favorite), the Dales and York. Additionally, I grew up often visiting my British grandparents so new locales are appreciated. Surprisingly, I've never been to Wales and Cardiff looks to be a great option. Day trips are really our only option as our time to visit our son is limited to 1 week.

You can go to Cardiff from Bath by direct train - at hourly intervals & takes just over 1 hour - but be sure to check for engineering work as these routes are currently being electrified. www.nationalrail.co.uk

It also takes just over 1 hour to drive to Cardiff.

These sites are relevant to the Cardiff area but you would not be able to see everything in 1 day.
http://www.visitcardiff.com
www.cardiffcastle.com
https://museum.wales/stfagans/ (5 miles west of the city centre - bus 32/320).
http://cadw.gov.wales/daysout/caerphilly-castle/?lang=en
http://cadw.gov.wales/daysout/castell-coch/?lang=en

I agree with exploring the canal. We hiked along it extensively on a 4-day walk to/from Bath and thoroughly enjoyed it. We walked to Bradford-on-Avon (charming), Lacock (double charming), and Castle Combe (even more charm). So you might wish to drive to those villages. But walking along the Right of Way was a fantastic experience, even in the rain.

The two Bath tidbits I would add:

Thermae Spas are wonderful and (depending on the timing) have specials that include a meal plus extra soaking time. We did this the day after we flew in and it was a wonderful way to reset the body clock.

Edington Church - Small town (about 20 miles southeast of Bath and halfway between Bath and Stonehenge). The church there is absolutely stunning. Built in the 13th Century and still used every week (and it's open to the public during the week).