There are several Budget locations within San Francisco itself and I'd encourage you to look into one of those. Another thing about renting from SFO is they have a massive user fee (11.11%) plus a fixed $20 charge for airport pick-up.
Alternatively, you could also use one of the locations near the airport (I see one in San Bruno, Belmont and Palo Alto, all taxi distance) that must be cheaper.
I'll add that picking up in San Francisco could also save you a night or more parking in a hotel which could be good. If you have days where you know you're just going to be in the city and won't need it, that's a great way to save some $$. Overnight hotel parking can be north of $35 per night.