Carlsbad Caverns National Park is located near Carlsbad, New Mexico, and can be reached via U.S. Highway 62/180. It is about 18 miles (29 km) southwest of Carlsbad, New Mexico. The driving distance is 149 miles (240) east of El Paso, Texas. There is only one entrance road to the park, the Carlsbad Caverns Highway.

Map of Carlsbad Caverns National Park and roads NPS file
If driving an RV, there is ample parking in the west parking lot, which is the first parking lot you'll see on your left upon arriving at the visitor center. Pull to the rear of the lot for RV spots.
Carlsbad is served by Greyhound and TNM&O bus lines. Major airlines serve Roswell and Albuquerque, New Mexico, and El Paso, Lubbock and Midland, Texas, all of which offer rental cars. Rental cars and taxi service are also available from the airport in Carlsbad.
Speaking of cars, the closest towns for refueling your gas-powered vehicle are White's City and Carlsbad, New Mexico (0.4 miles / 0.6 km and 20 miles / 32 km, respectively). If you are driving an electric vehicle (EV), chargetotheparks.com reports a few EV charging stations within 57 miles (91.7 km) of the park.