If you're planning on crossing into Mexico, the crossings at Juarez reached via El Paso or Santa Teresa are far busier than the one near Columbus, with all that that entails -- longer lines on the US side, but more to do once you're over the border. The mercado is busy, schlocky, and colorful. One warning: drinking age in Juarez is 18, and on weekends, many younger students at New Mexico State University in Las Cruces, and at colleges in El Paso, make the pilgrimage to indulge. Traffic back into Las Cruces can be frightening at such times. Be cautious.
Some destinations in other states that are close to their borders with New Mexico and hence reachable as day excursions are clockwise from the southwest corner:
Arizona
The Grand Canyon state borders New Mexico to the west, making Chiricahua National Monument, Petrified Forest National Park, Canyon de Chelly National Monument and the Navajo Nation good day-trip options.Utah
Located to the northwest, this state contains some of the most impressive landscapes on earth. Hovenweep National Monument, which extends into Colorado, is a daytrip possibility.Colorado
The Rocky Mountain state borders New Mexico to the north, offering opportunities to visit Mesa Verde National Park, the scenic railroad in Durango, enjoy Alpine skiing areas closest to the state line are Durango Mountain and Purgatory near Durango and Wolf Creek near Pagosa Springs, explore the Sangre de Cristo Mountains, known in Colorado as the Sangre de Cristo Range, which contain several "Fourteeners" mountains with summits over 14,000', or visit Great Sand Dunes National Park.Oklahoma
Sharing a tiny border in the northest, Black Mesa, the highest point in the state and a pleasant hike, is literally a stone's throw from the state line near the tiny town of Kenton OK.Texas
The largest of the lower-48 states, Texas is located to New Mexico's east. The towns of Amarillo, Lubbock and El Paso are all easy daytrips, as is Guadalupe Mountains National Park.