The Nut Tree Boulders, aka the Vacaville Boulders are directly inside an Open Space District and one of the closest outdoor climbing areas to Davis. The location features tons of boulders and over 300 problems. The rock is basalt and most of the boulders are a bit on the smaller side, so lots of traverses and short, hard, bursty, power problems. The area has lots of rolling hills that often make the boulders hard to spot from a distance. A good guide/guidebook or an exploratory state of mind is recommended to get the most out of the area. The space is shared with cattle half the year, though the main nuisance they provide are the piles of cow patties. While the problems are not very impressive when compared to a nationally renowned bouldering area, the proximity to Davis makes them a very worthwhile visit. On a clear day, from on top of the hill, you can get a great view of Sacramento and the Sierras beyond.
Start out heading west on I-80 towards Vacaville. Take I-505 North and exit at the first exit, Vacavalley Parkway. Turn left onto Vacavalley Parkway and drive straight until you head directly into a hill full of boulders. You can park right there and head to the closest boulders or there are also other access points to other ends of open space area off some of the neighboring streets (look for the Yellow Gates). While the open space district is fenced in, it is open to the public and gates do exist every so often, so no fence jumping should be required.
This is a link to a Google map with major features and access points.
Chris Summits' Wine Country Rocks - Very basic info about the area.
Aaron Rough's Nut Tree Boulders - Great info, unfortunately it is currently not sold in stores.
Finding the boulders can be a little difficult at first. Once you're past the cattle corral at the entrance into the open area, look west for one of the tallest hills, it's got a bench on top. That hilltop is where you'll find the mother boulder, and is a really good place to use as a landmark for exploring the surrounding rocks. It's a bit of a hike just to get to that central spot, so long pants and a minimum walking shoe are good ideas. There's a lot of fun looking combinations, including a couple or mini-caves and overhangs, and its proximity makes it a great spot.