Depends what you're in to, really. The Waterfront's a good starting place for a night out and meeting people, or a meal if you're not too picky. The floating harbour has a lot or arty stuff in it these days. If you like theatre the Old Vic's pretty good, or the Hippodrome if you prefer the larger West End style shows. If you just want to chill in some nice open green space then you can't beat being up on the downs by the Bridge. Damned good views too.
If you get there fairly soon and have good weather you might be able to catch the Bath Boating Company before the end of season. I think they stay going until the end of September and possibly a few weekends after but it's worth checking. It means a trip to Bath, but it's one of the best days out in the area if you can find someone to go with.
Coming up in October it's worth going to see the Beach Race at Western-Super-Mare, and towards the end of month the Guy Fawkes Carnivals start in the towns to the South. Bridgewater is the best of them (the Squibs are fantastic), but Glastonbury and Wells a pretty damned good too.
Glastonbury is a fun place to go to. The ruins of the Abby are quite haunting, the Tor in the right sort of weather is stunning (less so in the drizzle), and if you're that way inclined you can visit the Pagan temple and chat to the nutters... erm... druids who worship there. It's also the best place in England, to my knowledge, of buying spells, skulls, stone/bone daggers, crystals etc etc. A couple of pretty good pubs too.
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People who can't even CDR right
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