A few things to do.....
Food! There are soooo many amazing restaurants in the Bay Area, but here are a few suggestions in downtown Berkeley: Comal ($$, yummy Mexican and cocktails), Lucia ($$$, authentic Italian pizza), Chez Panisse ($$$$, world famous restaurant of Alice Waters where California cuisine got its start, reserve a table a month in advance), Cheese Board ($, best pizza in Berkeley, live music), Gather ($$, great for brunch), Imm Thai ($), Ike's Place ($ great for a sandwich at lunch time), Tupper & Reed (amazing cocktail bar, make a reservation to get the full and immense menu)
Napa, Sonoma - wine country is only 1-2 hours from Berkeley. You could even visit some of Mapistry's customers, including Peju Winery, Ferrari Carano, Fritz Winery, O'Brien Estate, Bennett Lane Winery.
Theater - Berkley Rep, see a show at this Tony Award winning theater
Baseball - SF Giants - the Giants are playing the D-Backs on September 15th and 16th
Kayaking - Elkhorn Slough - amazing kayaking with seals, otters and tons of birds, 2 hours from Berkeley
Hiking - Muir Woods, Mt Tam & Stinson Beach - Check out amazing, huge redwood trees at Muir Woods National Monument. Go for a hike on Mt Tam, the Matt Davis, Steep Ravine and Dispea trails loop is beautiful. Finally take a walk or sit for a while on Stinson Beach.
Historical Tour - Alcatraz - Take the tour of this famous prison on an island in the middle of the bay. Definitely listen to the recording that guides you through the prison. Be sure to purchase tickets for the tour (and ferry) a few weeks in advance.
San Francisco! Just across the bay from Berkeley, explore this famous city.
Beach, Hiking & Wildlife - Carmel & Monterey - If you are interested in venturing a little further, these two cities (close together) have a lot to offer. Make sure to check out the beach at Carmel, Point Lobos Natural Reserve and the aquarium in Monterey. Just south of Carmel is Julia Pfeiffer Burns State Park (Big Sur), which is also amazing but roads were damaged in mud slides this winter. Check the website for current conditions before visiting.