UC Davis has a student Equestrian Center that is VERY close (within walking distance) of the vet med buildings. It used to be open to the public for boarding but a lot has changed there over the last three years, including a huge renovation of most of the facilities (which were pretty awful, sorry, but they were...) so now there are some really nice stalls and a HUGE covered arena.
I believe the new UCD EQC policy is that only students can board at the barn, I believe this includes vet students but you never know with them, they tend to change policies randomly...and its definitely worth calling ahead to get on a wait list or reserve a stall a month or two in advance. Rates are very reasonable, and there are also a large number of boarding barns within a 10-20 minute drive, some of them quite nice, though nothing really "A" circuit if you're into that lifestyle.
If you need something more upscale, Kelly Van Vleck has a barn at Rancho Murietta which is not too terribly far, I would def reccomend her if you had a show horse you wanted to board with a trainer nearby. Also Rudy Leone's sale barn is about 20-30 mins away in Sacramento. I know several undergrads who rode at Rudy's through the years there, don't know what the arrangement was but they did get to ride a lot of big jumpers!
If anyone needs more info on boarding/training in the Davis area just let me know... I'm happy to help out, and there are definitely a couple people you should AVOID, so feel free to pm me!