When locals and students need to get out, they often head to "The City" -- San Francisco. It's easy to get to by BART train and a logical next step of exploration -- assuming, of course, you didn't just come from there! Oakland, just south of Berkeley, is a large and diverse city as well, with many ethnic neighborhoods less frequented by tourists than those of San Francisco.
Smaller cities around Berkeley worth checking out include Emeryville to the southwest, Albany to the north, El Cerrito further north, and Walnut Creek to the east.
The hills above Berkeley and Oakland, including Tilden and Wildcat Parks, are easily accessible by foot, car, or bicycle, and offer many hikes with spectacular views.
Further out from Berkeley, you might consider striking out to Angel Island for the day or an overnight camping trip. Marin and Sonoma Counties are moderate drives from Berkeley as well. You might also try wine tasting in the Napa Valley. Northeast is Sacramento, the state's capital city.
