One of the most otherworldly scenes can be found in the dripping labyrinth of Carlsbad Caverns. You can drop into El Paso or Midland, or even get a headstart by landing in the little city of Hobbs, NM. Definitely take some time to see the Guadalupe Mountains while you're there — you'll get two parks in one!

For those ethereal dunes of the aptly-named White Sands, your best bets are El Paso and Albuquerque. Head a smidge east and you'll be in a different world entirely, because the mountainous Lincoln National Forest is right next door. 

Santa Fe is just a tad further than Albuquerque from the most famous parks, but still close enough for comfort. It also offers a side of history: Bandelier National Monument is just outside of town. Here, you can climb in and around a Pueblo city dating back almost 900 years.

And lastly, you've got a shot at one of America's most remote National Parks: Big Bend! It's still quite the drive from either El Paso or Midland, but that's as close as you can get by plane. So just take one look at those sheer canyon cliffs, and try to convince yourself it's not worth it :-)