You have to visit as many of the different neighborhoods as you can. Each one has a unique flavor to it:
North Beach: very upscale area, historically Italian neighborhood, also the original home of the "Beat" era bohemians. Great restaurants right in the heart of the city, Coit Tower, Washington Square, and Lombard Street are all definitely worth a visit.
Chinatown: much bigger and richer than the one we have in Seattle. Go to Cathay house for dimsum, you will not be disappointed!
Haight: the former hippie/counterculture area of San Francisco, now very upscale and trendy like the rest of the city. Check out Amoeba Records, the Panhandle Park, and the hot guys running through Golden Gate Park. Comparable to Seattle's Broadway area. Read Tom Wolfe's "The Electric Kool-Aid Acid Test" for a sampling of the personalities that used to live there. Also check out the Red Vic Bed & Breakfast for a very unique (and cheap) place to stay.
Mission: Great Mexican food, street art and a unique blend of barrio/hipster culture. 16th and Valencia streets are great for nightlife.
Downtown: Mostly high-end designer stores and skyscrapers in this area, honestly not as interesting as it sounds. Be careful in the Tenderloin/Civic Center area late at night. The homeless and drug addict population in this area is truly a sight to behold. Nothing spells instant sobriety like a walk down Market Street at 4am.
Castro: Gay center of the universe, much more neighborhoody/intimate feeling place than Seattle's Capitol Hill. I can highly recommend the Cafe and the Lookout on Friday and Saturday nights (crowded w/ strong drinks and great eye candy). Q Bar is like Seattle's Kurrent, a mix of gay/straight folks with dollar drinks all night on Mondays. "The Mix" is a great low-key gay bar on 18th street with an outdoor patio. 440 is good if you're interested in guys over 30.
Last thing: BEST HOTEL DEAL EVER: Mosser Hotel 4th and Market Street: 70 bucks a night for 3 star hotel, not bad in one of the most expensive cities in the country.
Enjoy your trip!