As far as checking out quilt stores without a car: you could take the train down to San Mateo and get a cab. There is a quilt shop there called Always Quilting (alwaysquiltingonline.com). Try this one called Quiltworks and see if they are still in business in SF:
http://www.quiltworks.org/. A third one if BART goes near there and I think they do, is New Pieces in Berkeley.
Unfortunately, most of the quilt shops in SF proper closed before I left the Bay Area 5 years ago. As far as things to do, VernaL has it right. Check out the deYoung Art Museum. The Science museum was rebuilt and it is very cool. The zoo and botanical gardens are nice. There is also a Japanese Tea Garden.
Fisherman's Wharf is very kitschy touristy, but it can be fun. Chinatown and Japantown can be fun.
Citypass is another option that my DH and I have used in other cities. Here is the link for SF:
http://www.citypass.com/san-francisco. It does cover a nice selection of sites to see.
Have a good time. One last thing, bring warm clothes. It does get cold (high 50s during the day) in February, especially with the wind.