I feel really bad because I saw your post the other day, historyenne, and I couldn't think of anything to suggest... despite the fact that I was born in Bristol and have lived in the local area my whole life!! Problem is, most of the stuff I do in the city is everyday stuff, like shopping, visiting friends, going to the pub, going to work etc. (I'll be in the city centre all week, but only because I'm doing jury service at the moment!) so I never see the touristy side!
sonofasailor has some good suggestions, although just to warn you that Bristol Zoo admission is quite pricey (I haven't been to the zoo since I was 7, on a school trip, and so when I looked into their prices a couple of years ago, I couldn't believe the cost!), but the museum is free to visit (I haven't been inside since I was a kid, but my parents went last week and said it was really good). Another thought, if you haven't done it already is a visit to the SS Great Britain (
http://www.ssgreatbritain.org/Home.aspx).