It’s a wonderful city. Much bigger and sprawling than Bath, quite hipster in places - a big, buzzy, arty city with all the pros and cons that brings.
Trains from Bath will come into Bristol Temple Meads, which is a bit of a walk from most of the city attractions. You might want to grab a cab or bus from there.
SS Great Britain is outstanding - not cheap, but definitely a highlight. You might also want to go up to Clifton Suspension Bridge for a look.
If you’re interested in street art, Bristol is the home of Banksy so you could do a walking tour. The cathedral is also worth a visit, and there are a bunch of interesting museums: M Shed (not far from SS Great Britain) is a kind of museum of Bristol, lots of activities and stuff. Plus there’s a much more traditional museum/art gallery at the top of a hill near the university/Wills Tower.
Loads of great food - as you’d expect from a big student city - but because the city is quite spread out it really depends where you’re going to be.
St Nicholas Market is good for lunchtime street food. https://www.bristol.gov.uk/st-nicholas-markets
It’s a very different place to Bath, which is much more preserved in aspic, but makes a great contrast.