Hi, I also was just accepted to Davis and I'm strongly considering accepting the offer. Right now I'm living in West Sacramento so I wouldn't have to relocate, though I am thinking about moving over to the mixed-income lofts in Midtown Sacramento where I would pay just a bit more on rent, but be surrounded by everything I could ever ask for. I personally don't think I want to live in Davis, because I really like living close to Downtown and Midtown Sac and all the other great neighborhoods. I do have a car, but I rarely use it, as I bike commute to work. If I go to Davis I'll probably do a bike-bus combination commute, and I'm not anticipating that it'll be that much of a hassle--I understand why the professor said a car was "essential" since Davis is somewhat isolated and public transit isn't optimal in the area AND who doesn't want to sneak away to SF every once in awhile? But honestly, I think you would be ok, especially if you have a bike.
As for your stipend, I am an AmeriCorps member currently and make just a hair over $10k/year and I'm doing absolutely fine. My rent in West Sac, which is cheaper than just across the bridge in Downtown, is about $400 and it's a really nice neighborhood, and like I said it's just across the bridge from all the action, and I still have enough to buy all the delicious food and beer I want and to go out a few weekends a month. I'm not sure you'll find a rent price that low in Davis, though. It sounds like you've been surviving on a penniless lifestyle; 16k is more than enough once you get a good living situation locked down. So I would say, look at either West Sac or some of the affordable rental housing options in Sacramento--go to this link http://www.shra.org/WebReports/AffHousing/htmProjectListing.php for a list of options, but research the address to see what neighborhoods they're in, because some are in the hood.