Alright, so, as a former drama major, I might not be the most impartial judge, but I would say that seeing a drama department show gives you the best opportunity to see good theater in the Stanford area. The scripts done at Stanford are consistently riskier and more engaging than the pieces at nearby Theatreworks in Menlo Park. Not every drama department show will be great, and not every show will be good, but they will all be cheap, and almost all of them will feature a few excellent performances.
Check out drama.stanford.edu to see what's on during your visit. In general, the undergraduate-directed shows are more entertaining than work done by grad students. After all, the majority of the undergrads are fueled by nubile hopes of future success, whereas many of the PHDs have recently failed at having careers. Also, beware of anything described as "darkly erotic." Chances are, you won't see anything more risque than a girl's bare back, and you won't get to hear any jokes.
On the Stanford campus, there is not a lot to do on a weekend between dinner at 6pm and parties at 10pm, so even if you don't usually go to theatre, it's worth an hour or two of your time to check out whatever is playing.