Aside from being a great destination for camping and rock-climbing, City of Rocks State Park has about 7.5 miles of well-maintained singletrack trails that go around the perimeter of the rock formations: The Hydra Hike an Bike Trail system. In addition to these well-signed trails, there are numerous, unsigned and legal free-ride options within the City of Rocks.
A good map of the trails can be obtained inside the Visitor's Center (V.C.). There are also bathrooms, showers, and water available at the V.C.
The singletrack trails are mostly beginner level, however there are trickier sections that will test aerobic and technical abilities of experienced riders. Best way to ride the trail is clockwise, beginning at the botanical garden located about 500 feet west of the V.C..
Beginning in the south side of the park, the trail starts out wide and fairly easy. After about 3/4 mile, you come to 5-way intersection: take the trail that leads south. This takes you to a rocky 1/2 mile singletrack section that eventually links back to the 5-way intersection. Once back on the main trail, head north into a fast, false flat, winding singletrack section toward the north end of the park.
Trail will eventually lead east and then drop back south down a fast, windy, pea-sized gravel section with options for lots of speed and/or washing out around tight corners.
Important note: There is an out-and-back option you can take to ride up to the top of Tabletop Mountain northeast of the park. Before heading down the east side described above, you will see a cairn with a painted yellow-top. This well-marked trail heads through a gate and follows the base of Tabletop Mountain, north then northeast before pitching drastically up the mountain. This is probably a hike-a-bike situation for even the fittest rider. Once atop the first tier, you can ride along the edge until you have to get up the second tier to the top of the mountain. Once again, even the fittest of riders will probably have to push their bike up to the top. The good news is that the view is awesome from the top of the mountain and the ride down is 95% rideable (but very technical), so you will not have to carry your bike back down the mountain as long as have decent technical skills and nerves of steel.
Back to the fast windy, pea-gravel section...
Once at the bottom, you have another out-and-back option: Up to Observation Point. This is 100% rideable. Probably the most demanding aerobic section (aside from Tabletop Mountain). This is fun uphill, switchbacking climb with a nice panoramic view of the surrounding mountains waiting for you at the top. From here it's back down toward the V.C.
As I mentioned above, there are also numerous freeride options on slick rock in the park that will definitely test your technical skills. Best part is that it is truly freeride. You point your bike and go!
Summary: Fun trail system with amazing scenery all around. The trails really are just a bonus to everything else here. The ideal situation would be to camp here and bring your bikes for a fun diversion from all the rock climbing you will do. Not sure I would drive more than an hour or so just for the trails themselves, but camping, hiking, climbing and biking? Absolutely!
The out-and-back trail up to Tabletop Mountain is pretty cool for the experience of getting up there, but after doing it once, I probably would only ride to the very first point when it becomes hike-a-bike and turn around at that point. Not sure how worth it is to haul your bike to the top just for a view and a screaming downhill ride. Basically imagine walking your bike up that mountain and use that to make your decision whether it is worth it for you.
Everything else is 100% rideable and fun though. Great little trail system that is well-maintained and with great signage throughout.
Aerobic: 3 (climb up to Tabletop an Observation Point will open the lungs)
Technical: Mostly fairly easy with exception of Tabletop Mountain and a rocky section southwest of Visitor's Center.
Overall: 4 (fun trail system with amazing scenery)
Recommended Route: The map you get from the Visitor's Center recommends riding in a clockwise direction, and after riding it, I would definitely agree. The biggest bummer would be riding uphill on the east side where all the pea-sized gravel an sand washouts are located. They are fun on a slight downhill but would be a serious grind as an uphill.
Other recommended trails in the same area: There is supposed to be some great riding in/around the Silver City area, but I am not familiar with any of those trails. In Las Cruces: Dona Ana trail system is pretty nice.