You chose a fantastic city to get a US introduction!
Avoid the Fisherman's Wharf by all means. Sure, Alcatraz is cool and the Aquarium of the Bay is ok, but the general area is so frustratingly touristy that I almost have panic attacks when I go there. I hate, hate, hate it there. They do have an In N Out there, though.
Bars/drinks: Toronado in Lower Haight is my shit. A LOT of taps, history, awesome dudes behind the bar. A fun place to watch a Giants game or to just get drunk in the middle of the day. Lower Haight itself is a great drankin' area - you'll find a lot over there if you just keep an open mind.
If you want to have a fun night of drinking, do Chinatown. Most Chinatown visitors like seeing the place in the day because the culture is something else over there, but I love it there mostly for its guaranteed nights of drunken fun.
Food: Depends what you like, SF has everything - I honestly believe it's is the second-best "food city" in the US behind NYC. House of
Prime Rib will set you back $50 each, but its hype is fully warranted. Seafood options are plentiful, just do a little research online before you settle on a place because anywhere can sell frozen fish, but good, fresh fish (crab in particular) is different.
Bike across the Golden Gate. It's kind of a stereotypical SF thing to do, but I admire that bridge so damn much that it's worth it to me.
Golden Gate Park is beautiful, but the "main attractions" (Flower Garden, Japanese Tea Garden, etc.) cost money, so plan accordingly.
Enjoy yourself. SF is the Dublin of the States; people are friendly and want to talk to you about their great city. EVERYBODY has their favorite spots/activities, so don't be afraid to ask a stranger you meet "Got any suggestions?"