Getting around San Fran can easily be done by a combination of walking, cable cars (expensive but you have to take at least one ride while you're here), BART (the subway around here- bart.gov), Muni (the bus line- EVERYONE who has put any time in on the Muni has a story to tell...), & street cars.
Neighborhoods to check out:
* The Mission (Mexican/Latin American quarter)- great authentic Mexican food, the best murals in the City, & a fun vibe- stick to Valencia St (being directly on Mission St @ night not advisable; it can be seedy)
* SOMA (South of Market)- some good museums here (SFMoMA, etc.); some places here are also sketch at night, so watch it
* Financial District- not too much that's greatly impressive, but make sure to stop by the Carnelian Room in the Bank of America building for some of the best views of the City
* North Beach- no beach here now (although there used to be), but good Italian food & interesting (the ostensible Italian quarter, also birthplace of the Beat movement)
* China Town
* The Castro- perhaps nothing fulfills people's stereotypes about SF more...
* Haight-Ashbury- hippy central in the 60s, still a decent amount there now too (& dirtbag kids panhandling)
Other things to check out:
* Baker Beach- great views of the Golden Gate
* The Presidio
* Twin Peaks- some exceptional views of the City
* Painted Sisters- postcard view, with some fine examples of San Fran's famous Victorian architecture front & centre
* Golden Gate Park- the W coast's answer to Central Park
* the Golden Gate (duh)
* Fisherman's Wharf- a tourist trap, but you still gotta see it- where the fishermen come in with their catches
Some museums worth checking out: SFMoMA, Palace of the Legion of Honor, Asian Art Museum
Not too far from SF:
* Mt. Tamalpais- beautiful area, wonderful hikes (Steep Ravine & Matt Davis trails make a really nice loop)- stop by Stinson Beach while you're there & have some seafood. Tennessee Beach is a great short hike close to there too that offers beautiful views of the ocean, the Marin Headlands, & even the tips of SF skyscrapers & GG bridge too from the right vantage points
* Pt. Reyes- one of the greater Bay Area's natural gems- stunning
* Mt. Diablo- you can get a taste of what things are like somewhat inland (think hilly oak environs, not found in SF (similar to the environment of the western Sierra- oak-y grasslands). Some very nice hikes from Clayton on the N side, & exceptional views.
Would also highly recommend driving N for a few days- Mendocino, Fort Bragg, Eureka, Arcata, Humboldt County, Avenue of the Giants, Redwood National Park, etc.
Will try to rack my brain for other ideas...