BATS is the Bay Area's biggest improv theater, which makes it kind of a hybrid between a comedy club and regular theater where you'd see a play.
Their schedule includes a lot of different types of shows. If you're looking for straight up funny, I recommend their Theatresports show where two teams compete in different challenges. (It's a little like "Whose Line is it Anyway?" and the scenes move pretty quick.) These shows are a particularly good date night since there's lots of funny stuff happening, you get a chance to shout out suggestions, and there will probably be something to talk about after the show. (Plus, some of the stuff they do on stage can be a little dirty and you'll learn what sort of sense of humor your date has by the way he/she responds!)
If you're looking for more of a theater experience, try one of their "long-form" shows. This is like a regular play, but it's all made up completely on the spot based on the audience suggestion. It's pretty incredible really. These shows vary in tone and style--everything from improvised Shakespeare, to Star Trek, to family drama, to musicals. Check their schedule to find something you might like.
And, with tickets in the $12 to $15 range, its a pretty good deal for a night out. I recommend BATS Improv!