I live here, so hopefully can offer a few pointers.
The Roman Baths are great, and if you’re art-curious the Victoria and Holburn galleries are great, and you get to walk down Great Pultney St between them.
The Royal Crescent is worth seeing, and if you fancy a walk you can walk up to Lansdown Crescent fora pretty good view. Alexandra Park, on the other side of town is also a great vantage point (but not much to do once you’re up there).
There’s some great walks – you can amble out to Bathampton and beyond along the canals, or the Two Tunnels out to Midford, and the Bath Skyline walk is worth it as well.
EDIT: Oh, and if you’re going to the match allow lots of time to get into the ground and to your seat if you’re getting a beer!