Hi Sarah,
Golden Gate Park is going through some renovations of the museums so the aquarium is out for now. The surrounding area is full of cool places.
The Inner Sunset has Marnee Thai. The chef won an award from Thailand's prime minister/president for his Pad Thai. Also Arizmendia Bakery is on 9th between Irving and Judah. Great coop bakery with killer cheese rolls and fresh pizza.
Cole Valley has some nice cafes & restaurants including Kezar and Cafe Reverie.
Haight Ashbury is accessible at the foot of the park near the panhandle. You have another Kezar Pub (Best place to catch a soccer match/Red Sox game), Cha Cha Cha, Zona Rosa Burritos, Amoeba Records, Ben and Jerry's.
For a great view of the ocean at sunset you can visit Beach Chalet Restaurant and Brewery. Hot view and good beers, plus live music.
Beach Chalet Restaurant and Brewery
Map of GGP
Local weekly newspapers like the SF Weekly and Bay Guardian are good sources of other events. The best source though is Craigslist.
Have fun, SF