San Francisco's Civic Center hosts most of the city's wide, sprawling government buildings. City Hall is located here, as is the United Nations Plaza, the headquarters of the Supreme Court of California, and the main branch of the public library.
If you want good inexpensive food and you want to help local agriculture, you can stop by for the San Francisco Heart of the City Farmers Market. It's active on Wednesdays and Sundays, 7AM-5PM, on Market St. (between 7th and 8th St.), year-around.
Also see the Civic Center Farmers Market.