Hey there - not a resident, just a medical student, but I lived in LA for 7 years up until this past summer, and almost went to UCSF for medical school (so I was looking at prices there just a mere 6 months ago).
Sooo... first off, Craigslist is a great resource for both LA and SF apartment hunting.
I lived in LA proper (which tends to be even more expensive), not by Harbor, but my best guess would be $700-$900/mo for a studio depending on exact location, building type (big complexes w/ amenities always seem to cost more).
Add at least $100-$200/mo to that for SF.
Good luck, and I'm sure some people will post soon with more accurate figures!
Hmm..... seeing Darksideallstar's post, perhaps I was a bit too optimistic about SF..... When I was looking, though, I was definitely going as cheap as possible (nothing more than a studio) - but yeah, as I recall, you probably won't find much for under $1000 in SF. Good luck!