I'm living here right now and actually share a 2 bedroom apartment with another guy in an apartment complex with mostly graduate students/post-docs. I pay about $700 for my own bedroom, not including utilities or anything. I would say $800 a month is definitely do-able and pretty much everyone, including professors, bikes to get around here. From my experience, I've found the closer you live to downtown Davis and the campus, the older the buildings tend to be. Another option is to consider living in downtown/midtown Sacramento and driving or taking the Amtrak train over to campus -- this could take anywhere from 20-45 mins depending on traffic if you're driving.
Check out http://daviswiki.org/ for lots of useful information.