If you get hungry in Deming, keep driving…
In Las Cruces, there are great restaurants near the highway. Take the Main exit (turn on University) to get fresh roated coffee at Milagro (University and Locust). Also located on University is The Phonecia Mediterranean Restaurant and for quick decent Chinese try 5 Brothers. A block North of University on El Paseo, you’ll find a surprisingly good Thai Restaurant – The Lemongrass.
Take the Avenida de Mesilla exit, and visit the historic town of Mesilla. It’ll give you the best “authentic” New Mexico experience short of Taos or Santa Fe, and it’s located a couple miles from I-10. Dine at La Posta or Andale’s (both located off Av. de Mesilla) for your obligatory green chile experience. Grab a cup of decent cup of coffee at the quirky Bean.
If you want an interesting drive, take Highway 28 (Avenida de Mesilla) to El Paso instead of I-10. You’ll pass through the World’s largest pecan orchard, Stahman’s Farms. Stop in the gift shop if you want a sack of fresh pecans. Highway 28 will put you in a calm state of mind before you try to get through the freeway mess of El Paso.