San Francisco is one of the few US cities where car-free living is practical for many residents. Hayes Valley, the Mission, Nob Hill, and Russian Hill all combine dense retail with multiple Muni Metro and bus lines.
Hayes Valley, the Mission, the Castro, Nob Hill, North Beach, and Russian Hill score the highest. All combine grocery, transit, parks, and restaurants within a few blocks.
Muni Metro covers Market Street and key corridors. BART connects to the East Bay and SFO. Cable cars run on Powell and California. Most central neighborhoods are well-served by frequent buses.
Caltrain corridor (Mission Bay, Dogpatch, near 4th & King) gives you the fastest peninsula access. Bernal Heights and the Mission have decent freeway access for driving.