Also, remember that East Bay near BART is closer to South of Market than most of San Francisco city is, time-wise
Depends what part of the East Bay, of course. West Oakland is the closest BART station, but it is in some serious ghetto. Lake Merritt, Berkeley (esp North Berkeley) and Rockridge are your first good options, but they'll take a little longer to get to. My advice would be definitely to check out Rockridge, it's a surprisingly nice part of town.