For a not too expensive hotel in San Francisco near the airport, I'd totally recommend DoubletTree in Burlingame.
Do rent a car in San Francisco, I've always been able to find excellent deals there for small compacts w/ unlimited mileage. The Bay Area is even more spread out than Calgary. Golden Gate Bridge, Park and other touristy areas aren't too far, 15~20min drive from airport. If you're after lesser known stuff, maybe instead of Chinatown, head to Richmond area near Balboa or Cabrillo Street, there's a large'ish Chinese population residing in this area. Still somewhat touristy, but not quite as well known, the Cliffhouse Restaurant is neat to check out especially if you have a lady friend with you for dinner, great view of the ocean and you can see windmills there too.
If you want to see the ghettos, the West Oakland area is where you'll want to be. Things are really quite divided, it's like there's a literal "wrong side of the tracks". Not too far from the ghettos, is Fentons Creamery my favorite ice cream shop. Up the street from that is Mountain View Cemetery. Really massive, old and serene, you'll often find joggers through out. Much nicer places than the ones I've seen in Calgary. I think they actually have guided tours sometimes.
If you're driving an hour South to San Jose, maybe you wouldn't object to driving another hour further South to check out Monterey Bay Aquarium and nearby Mazda Raceway Laguna Seca.
Someday we may need to activate the halo structure off Deerfoot and destroy the North East.