Try hotels in San Bruno, which is located on the west side of US 101 from the airport. Even without a day rate, you'll probably not pay more than $75 for a room, including tax. For instance, the Howard Johnson San Bruno/SFO West is currently going for $61 per night and gets decent recommendations from Travelocity and TripAdvisor. There are similar hotels with similar rates and ratings in the nearby area. I suspect San Bruno is just far enough away from the airport that the rates have dropped a bit yet you get a fair amount of the same amenities you look for in an airport hotel--such as a regularly running shuttle to the airport. San Bruno has a BART station in case you find a couple of hours sleep sufficient and want to have an early dinner in SF.

The big issue is simply being able to check in at 11 a.m., but I'm sure hotels near airports are used to this and try to clear some rooms for this purpose. For this reason alone, I'd consider a direct call to the hotel to explain your special needs so that they can set aside a room as soon as possible. I mean, when you're in a hotel for a regular stay, haven't you wondered why the maid sometimes comes by at 8:15 a.m. and knocks on the door?