Saturday is the classic waterfront day: reach Powell, ride cable car, see Fisherman's Wharf and Pier 39, eat chowder, do Alcatraz, then dinner in North Beach. Sunday is culture plus icons: Carnaval in the Mission, Painted Ladies, Golden Gate Park, Japanese Tea Garden, then Golden Gate Bridge before returning to San Jose.
Book Alcatraz first. If Alcatraz is sold out, use that time for Coit Tower, more North Beach, or a bay walk.