I haven't been to L.A., but I have been to the Bay Area, and I would say I could spend a week there finding stuff to do, easy. I'd probably spend a day or two in Santa Cruz if I were staying in San Jose and I had a car. The road from San Jose to Santa Cruz is a bit scary, though, so I would avoid it if you aren't comfortable on a winding freeway with heavy traffic (depending on time of day, of course). I'd probably take a day and go to Great America and ride all the rides I was too chicken to ride the first time I went.
There is a lot to explore in San Francisco itself. I like Golden Gate Park a lot, and the beach nearby attracts its fair share of surfers and kiteboarders. Fisherman's Wharf is always a must visit for me despite the touristy nature of it mostly due to sentimental reasons, and while I'm there I always visit Ghiradelli Square and have a hot fudge sundae (it's a family tradition). If you like books, you HAVE to visit City Lights Books in North Beach:
City Lights Books Vesuvio, a little nook nearby, is a good place to grab a beer. A place I haven't been but I'm dying to go to is the farmer's market in the Ferry Building:
Ferry Building Marketplace Chinatown is also worthy of a lengthy exploration. San Francisco is really a city to be enjoyed on foot with no specific destination in mind sometimes; it's best to take it easy. Walking is not always the best, though--there are a lot of steep hills, and so the cable car is not just a tourist attraction, but a great way to get up the hills. There are a lot of colorful, interesting neighborhoods that one could easily spend a whole day exploring, so yes, you could spend a whole week in SF itself, but there are other things to be done in the wider Bay Area.
Another day can be spent exploring Berkeley (funky, fun, and interesting; also home to one of the coolest cheese shops I've ever been into, and a great bookstore I don't remember the name of--I'm sure genuinegirly knows), and yet another poking around Sausalito (accessible by ferry from San Francisco). One of my favorite things to do in Sausalito is to have a tasty beverage somewhere with a view of the marina, and just watch the boats.
And if you do have a car, you could always go out to Pacifica, eat at the Taco Bell on the beach, and watch the surfers.