Well you should probably visit Guitar Center. I'm not a big fan of GC but the one we have here is pretty friggin huge. They have an entire floor dedicated to drums, tons of amps and guitars etc. Might as well check it out while you are here.
Some other places you should check out:
Panhandle guitars - This is a small shop with good prices. Most of the stuff he has isn't that great but he does get some really good used stuff in from time to time. I got my 73 Les Paul here.
Rocker Guitars - This is a small/mid sized shop with lots of great stuff. Dr Z amps, Soldano, THD etc Lots of great guitars and a great selection of pedals. Everything here is on the pricey side but it's all great stuff so it's worth it if you have the $$.
Guitar Solo - This is a small shop that specializes in acoustic guitars only. They also publish classical guitar music and have TONS of it. Cool little shop.
Black Market Music - This place has tons of used stuff. He gets some really good stuff in from time to time. Chris, the guy who owns the place, is funny as hell - likes to talk sh!t about everybody's mom. This is where I picked up my Stiletto. =)
There are a bunch of good bars and clubs here but unfortunately you'll have to be at least 18 to get into most places. I'm pretty sure that a club called 'The Bottom of the Hill' has all ages shows from time to time you might want to look that up.
Some other stuff... let's see - there's Alcatraz which is a somewhat interesting day trip. If you want to go there make sure you make reservations in advance or you won't be able to go.
Other than that... um... you'll probably want to check out Golden Gate Park and Ocean Beach. Golden Gate park has a bunch of stuff in there - gardens, an art museum etc..
Eh... I don't really go out much anymore so I don't know what else to recommend. If you have anything specific you are wondering about just ask!