The East Bay Regional Park District (http://www.ebparks.org/) maintains 65 parks across the East Bay, ranging from easy access picnic areas to off-limits wildlife sanctuaries. More than a dozen campsites range from "family camping" to backpack areas.
East Bay fans love sports; you can see pro teams in Oakland, across the bay in San Francisco and in the south bay San Jose. The CAL Bears play at UC Berkeley (http://www.berkeley.edu).