Thanks for all of the information so far. It's really, really helpful! Based on some suggestions here, I'm looking to fly into SFO and spend 3-4 days in the city, then rent a car and drive up to Sonoma and stay in a B&B (I've found a couple good deals so far). Maybe a day to drive up to the Healdsburg area and do a few tours, then another day to drive out to Sonoma Coast State Beach and hang out in Sonoma or Napa proper. Finally, one more day in the area (maybe somewhere between Sonoma and Healdsburg?) doing some more tours, possibly having a picnic or something.
Still working on the San Francisco portion of the trip, but I'm thinking maybe some walking tours or the Modern Art Museum? Open to suggestions.
FWIW, I'll be flying from EWR to SFO; seems to be the best option price-wise at the moment.
For SF:
MOMA is actually closed for remodel but some of the exhibits have been moved to other locations.
If you like architecture City Hall is pretty nice.
Golden Gate Park has museums and gardens.
My wife loathes Fisherman's Wharf as a tourist trap. It is a tourist trap but if you feel compelled it is kind of cool but still very tourist trappy.
Saturday, Tuesday, Thursday is a farmer's market at the ferry building.
From the ferry building can take the cable car up California, get off and walk around Chinatown.
Golden Gate bridge obviously, I like the view from the north side.
Twin Peaks if it isn't foggy is a great view of the city.
Alcatraz is popular so you probably want to get tickets early.
Painted ladies, Coit Tower, Lombard street are all popular.