Not a whole lot. Most of the sightseeing stuff are in SF. A few good shopping places not too far away that might interest your girlfriend: Stanford Shopping Center (Palo Alto), Santana Row (San Jose), Westfield Valley Fair (Santa Clara), Great Mall (Milpitas).
I stayed at the Fairmont during the week I spent in San Jose and I loved how it was "central" to most of the downtown action (or at least that's how it felt to me). The De Anza also looked like a nice place each time I walked past en route to HP.
Essentially, I highly recommend seeing the Winchester Mystery House, eating/drinking at the the Los Gatos Brewery and stopping by the Computer History Museum in Mountain View. The CalTrain and the "trolley" are easy to navigate and cheap to use to get out to the far-away attractions. Oh, and depending on how deep your wallet is, Santana Row is a must-see.
Finally, find the time to visit Stanford. They have free tours and great shopping all around Campus. It'll blow you away if you're used to Canadian Universities.
Drive down highway 1 between SF and Santa Cruz before the game (during daylight). Make a day of it. Make multiple pit stops along the way to see beaches or take hikes inland to bluffs (PM for details, if needed). If you like natural stuff you can spend the day like this. If you like man-made things you can check out the Boardwalk in Santa Cruz, or stop at a winery in Bonny Doon or on the SJ side of the mountains.
Once it's getting late, head over highway 17 (fun times ahead!) and eat phenomenal food in/around SJ (PM for details, if needed) either before or after the game. See game. Great day complete.
Can't count how many field trips I took there as a kid. Went back recently after enjoying some California medicine and it was even better than I remember!
Regarding the OP, I would say try to see some unique Bay Area stuff, specifically SF.
San Francisco: Alcatraz is a cool experience I would recommend it if you haven't been there. All of Pier 39 in SF is very cool and a great place to just walk around. If you are going to be here on a weekend I HIGHLY advise going to the Saturday farmers market at the Ferry Building in SF. It is one of the best farmers markets I have ever been to.
Here is a wiki list of way too much stuff, but it's categorized nicely.
One of my favorite museums in the Bay Area, I love it. But yeah, I'd join in with most and say spend most of your time in SF. SJ has a nice downtown, but I don't know that there's a lot to do (eat at Henry's Hi-Life).
Stanford is a gorgeous campus, but I'm a little biased.
Wait nobody mentioned Santa Cruz? Really? Anyway I sort of concur with the other posters San Jose is mainly just near everything you would want to see in Northern California. Thats the advantage. But seriously if try Pho in San Jose. I'd recommend Pho Kim Long and have lunch at La Villa you'll love it