One of the poorer and seedier parts of a rich city, the Tenderloin can sometimes be dangerous and, more often, unnerving.
Home to the city's biggest concert venue (the Warfield), Glide Memorial Church, the Exit Theater and Tu Lan, the TL highlights many of San Francisco's best qualities. Bourbon & Branch is a fun spot with great cocktails.
Adjoining Civic Center hosts most of the higher-brow performance beyond theater - eg, the Symphony, Opera and Ballet (and, uh, the art of City Hall)
Otherwise, "the loin" is easily accessible via BART and Muni.
Wikipedia: http://en.wikipedia.org/wiki/Tenderloin,_San_Francisco,_California