You're very unlikely to be able to find folks with RV parking space at their homes in the Bay Area that you could rent/borrow. You might be able to find something in northern Marin or Sonoma counties. Really if you want to stay in that area of SF, you'll be having to find an RV park to stay at and that means paying a monthly rent which will likely be more expensive than renting a house somewhere between Vallejo and Sacramento.
The reason you don't see RVs more in the city is because there are rules against them parking on the streets and few, if any, homes have extra land to park an RV - they barely have yards. And there are rules against living in an RV in a driveway, side/back yard even if it's OK with the homeowner.
That also brings the question of driving into the city area - are you going to have a car to get around? Or just the RV? Just an RV is not going to be conducive to driving through SF, Daly City, etc., on a daily basis.
An RV really isn't going to be a "money saving" reality in the Bay Area.