Dont bother with Ghiaradelli square, skip Pier 39, and Fishermans Wharf is only good for a quick stroll and maybe lunch. If youre looking for good California chocolate, find a Sees store- you wont be sorry.
Alcatraz is cool, but will take much of a day getting there, touring the site and getting back- make reservations in advance for both the park and ferry.
Coit Tower (up the hill from Pier 39) offers great views, but more importantly, the inside is decorated with depression era mural by WPA artists.
The cable cars are Ok for a trip up and around the hills of SF, but IMO not a must do activity.
Golden Gate Park often has free activities such as concerts, and has the De Young museum (check to see the What exhibits will be there when you visit), and a Japanese garden.
The Presidio is home to the Walt Disney Family museum with lots of interactive exhibits and personal memorabilia from both Disney films and theme parks. Check their website, reservations required. The well curated museum takes about 2 hours to cover every section.
I havent been to Chinatown in decades- if you have time it might be worth looking up restaurant recommendations, but not a must see IMO.
If you are a music fan/collector, SF is home to one of the best record stores in the world - Amoeba Records in the Haight Asbury district near the panhandle to Golden Gate Park. Lots of live music and nightlife - check local listings.
Theres a park where you can leave your car and walk across the Golden Gate if you want (or halfway there and back).
Good luck and have fun!