vaara's suggestions are really good rides that are short and will keep you in the Bay Area proper.
Expanding on those:
North: The Napa and Sonoma wine country areas have some great riding, and of course wine. All of the little roads that go east-west between those areas are nice country roads with little boutique wineries. There are also some bigger wineries with castle tours, picnic areas, and spas. A little further east from Napa will take you to rolling hills around Lake Berryessa.
East: if you want a longer trip, you could venture out to Highway 49 to see the Gold Country. Hwy 49 is below the snow line, and has lots of little historic towns like Placerville, Auburn, and Sonora. Yosemite and Lake Tahoe are in that area too.
South: For another long ride, you could head south to Monterey, Carmel, and the incredible cliffs of Big Sur where you are literally riding along the cliff's edge 100's of feet above the ocean. There are some cool tide pools you can stop along too.
In San Francisco itself, you could ride down the flower lined Lombard Street, which is supposed to be the most curvy road in the world. That will take all of 5 minutes, but is one of those must see things. It is a one way street going downhill through the 5 mph curves. Tell her you wanted to get her some flowers just before you turn onto the street, it will be all romantic and stuff.