Yeah, ignore the ignoramus from San Diego.
I would say, don't just stay in SF. If you're in good shape, the headlands, Muir Woods, the coastal trail and especially Mt. Tam State Park (Ridgecrest Blvd and the trails around it are among the most beautiful places on earth for my money. East Peak is nice too. For a taste of coastal Marin, Mt. Tam, Bolinas, and the Coastal trail heading south from Muir Beach are my picks. (I'm a Marin native, so I'm biased. Also, if you're here on the right day, the Pancake Breakfast at West POint inn (hike in only, built in 1905, so very old Marin) are worth it.)
In SF, yes, Chinatown, although for ambiance and dining, I'd be inclined to head to the Mission. It's a cool mix between old school SF (mostly on MIssion. and you absolutely MUST check out 826 Valencia. A fun little shop that benefits Dave Eggers' writing program for local youth! Also, breakfast at Tartine might be worth the wait, and Revolution Cafe has a taste of old Mission. For evening dancing and dinner, Baobab. ) and new hipster techy stuff (Ritual coffee, excellent!, Regalito is a fave of mine.) Also, there's a lovely little cafe right by the corner of Dolores Park that's delightful for breakfast. Of course, you should check out Mission Dolores itself, where it all began. The other original buildings of San Francisco are in the Officer's club also in the Presidio, which I believe is the very fist building in SF, dating to 1776.)
Taditch's is a worth while old school experience. (I think I'd skip the Pier 39, 41 stuff, except maybe for Musee Mechanique. Instead, if you want a sense of the intellectual style of SF, go for the Exploratorium, which is an amazing science museum which has had a number of big name local artists, cutting edge science and great education all in one place.
I'd also spend a little time in Golden Gate Park. It's an significant part of the city that's older than the neighborhoods around it. The De Young was recently redone by Herzog de Meuron. and the Conservatory, and the Academy of Sciences.
I would also consider the Presidio Social Club for a classic brunch (across the street from ILM where the star wars movies are made!)
More ideas coming