Berkeley is walkable in its core — the campus, Telegraph Avenue, and the Gourmet Ghetto are all navigable on foot. Above the flat area near the bay, the hills get steep quickly; walking up to Tilden Park or the Lawrence Hall of Science requires either a car or a serious commitment.
AC Transit buses cover the whole city. Bike-share (via Bay Wheels) is available and works well on the flatter streets. The hills above the campus are steep enough to make cycling difficult unless you're fit or have an e-bike.
BART's three Berkeley stations connect the city to the rest of the Bay Area efficiently.