Las Cruces, right on 1-10 on your way to AZ. The Dona Anas are the most popular and are great fun, you can piece together ~20 miles of riding without going over too much of the same trail. It's mostly a beginner trail, with a few challenging sections here and there. The Northern Dona Anas(NDAS) trail is short, at 6 or so miles, but can be made into a 20+ mile ride if you head north to Lucero via the turnoff at Lookout Peak (see map) after doing the loop counter clockwise. This ride is not too much of a technical challenge, but there are a lot of arroyos to cross, which makes for much climbing. I did somewhere around 2300 ft in 16 or so miles out there. That was enough to kick my behind, but I loved every minute. The Robledos(SST) is a technical rider's dream, but it has not had a whole lot of love, so it's iffy in spots, with pretty washed out sections. If you want a real challenge, the Robledos trail is the one. A-Mtn is short at about 5 miles, and it is quite popular with the hikers. It's quick, but a few technical spots on the north and west sides make it interesting. Sierra Vista is an out and back that is also kind of out of the way. It's OK, but personally I don't think you'll be missing much if you skip it. If you start from the north end, you'll descend nearly the whole way, and have the climb on the trip back. While I've never experienced damage there, I hear that it has claimed many tires.
Maps and directions to the trails can be found here -
http://www.lcrimrattlers.org/Maps.html
The DAs and NDAs parking areas are maybe 5 miles from each other, with the Robledos being 5 miles again from either of those - so driving from one to another is gravy, but if you have a high profile vehicle or a roof rack, you'll have to take the alternate route to the NDAs(which I can provide for you), or park just off Dona Ana road at the rail road tracks. All the trails are within 25 miles of each other. LCdaveH is also a pretty good repository of local trail knowledge, as well as a pretty cool guy. If you need to stop by a bike shop here for anything, I highly recommend Outdoor Adventures on Solano and Missouri. Those guys are outstanding.
Hope this all helps.
OH, just a heads up - March can get pretty windy here.