Your best bet is to rent a room Paul. There is really nothing that low here in the East Bay for that price if you are looking for an apartment short rent, maybe a studio but that is really pushing it.
I have a friend that lives in Hayward and he rents a room for $600.00 a month. You will not find an apartment for that low, if that is what you were looking for. He used Craiglist to find his room and it worked out quite well for him.
Oakland might be an option as HK has noted, but be careful some areas of Oakland are really bad. Lake Merritt, Piedmont, Montclair, Temescal, Claremont..close to Berkley are good.
You might also want to check Alameda as well, some nice areas there as well.