Old San Francisco is a part of San Francisco that remains as they were before World War III. It is mostly inhabited by Mutants since most of their kind are forced to live there. Tex Murphy lives in Chandler Avenue which is part of Old San Francisco (even though he's a Norm).
Although not mentioned so in dialogue, OSF seems to correspond to the NE areas of SF. As many of the destinations mentioned in the games are not specifically mentioned to belong to either NSF or OSF, it's possible that some of these also belong to OSF.