When downtow, get a MUNI day pass. It's $11, and it gives you unlimited rides on everything from the cable cars, the old street cars and the entire regular MUNI routes.
Seeing how a single cable car ride is $5, it's quickly paid for and you can easily roam around the city all day to see all there's to see.
Take the powell & Hyde cable car line from BART powell station and stop at the 'crookedest street' (Lombard) for a looksee, then grab the next one down to fisherman's wharf. Visit Pier 39, then take the old street cars back to the financial district from which you can take the California street cable car, or visit Chinatown.
The Cable car museum, along the tracks of the Powell & Hyde and Powell & Mason cable car lines is worth a visit too, and it's free.
There's just hundreds of things to see, 12 hours isn't enough. There's a tourism information desk at the BART powell station. Or you can grab tourist maps distributed freely in all the touristic areas.
BTW, during the day, there's often a long line to take the Cable car from the Powell turnaround platform. To avoid it, just walk up the track to the first stop and grab it there, they always leave some room for people to jump in from intermediary stops, and you won't have to wait in line like a tourist.
Off the beaten track:
If you're a ship lover, there's plenty of them to visit in the area. There's a WWII submarine, a liberty cargo ship, an old sailship and a steam paddle ship to visit.
And if you're a die hard aviation fanatic, you can go to Alameda and visit the USS Hornet, the WWII aircraft carrier which 'fished' Apollo 11 from the ocean. It's really worth visiting.
I'll do my own airline. With Blackjack. And hookers. In fact, forget the airline.