University Village is a nice place to live. A few of my friends lived their during their undergrad and it was relatively quiet with quite a few amenities. Only downside is that it's not close to campus, but Davis is a small city so driving/bus won't take too long.
Apartments are pricey because the cost of living in Davis is pretty high. If you're looking for a two bedroom apartment, here is a link that shows a few in your price range (http://www.apartmentfinder.com/Zip-Codes/95616-Apartments). As far as those apartments on J street, they're borderline decent and located near a homeless shelter I believe. The best apartments on a budget are Russell Park, Orchard Park, or Solano Park. They're cheap, right next to campus, and located near shopping areas.
Daviswiki.org is a website that'll be vital during your time in Davis. You can find information about almost anything, including apartments (http://daviswiki.org/Apartments)