From the BART station, take the MUNI (the "cable bus") - specifically the N-Judah outbound one. There is a stop right at UCSF. 🙂
Aerith is right about the N-Judah (though "cable bus" is a first for me). There's a BART station at the international terminal of SFO. Take it as far as civic center station. You exit and go upstairs. On that level, you'll see a toll station for MUNI. Enter there, go downstairs, and take one of the N trains. Make sure you're on the side of the platform (the northside) that says "Outbound". After a while, the N goes above ground for about a mile, then goes underground again. When it hits daylight a second time, you should be about four minutes from the UCSF stop. In case they don't call it out, the train makes a sharp left then sharp right and you'll see a parking garage on your left. That's the base of UCSF.
If you have downtime for 2nd look weekend, the nightlife in the immediate area is at 9th and Irving street, a five or ten minute walk from campus. Two bars of note are Yancy's (which has a fair amount of UCSF regulars) and Eldo's microbrew (right around the corner). The Inner Sunset, where UCSF is located, has a pretty small center and it's very easy to get a feel for the place. You'll be walking around the neighborhood where many first-time-SFers who get in to UCSF end up living.
The rest of San Francisco is easy to explore on foot and by public transport and doesn't take long. If anyone has any questions on where or how to get around, I'm happy to make a few recommendations; folks who've lived here for a long time have a tendency to really want to share the town. I'm sure they have time scheduled pretty tightly for second look, though.. My only plug is that if you head near Chinatown or North Beach, be sure to hit the Irish Bank, the City's best Irish pub (disclosure: my friend owns it and I occassionally would help out there).
I always picture UCSF's second look being a Preaching to the Choir sort of thing, but for those who still require some convincing, I'd strongly recommend spending a little time looking around our city. It's very small, very friendly, and very public transport friendly. It makes a great sales pitch for UCSF. I'm biased, but I really think it's one of the great places in this country to live.