The Blue Hole is an improbable spring/lake at Santa Rosa that's worth a look to break the drive along I-40 or if you're following the Route 66 tour. If for some reason you're hauling scuba gear across this arid terrain, you can break it out here or at nearby Perch Lake for an unexpectedly interesting dive permit required, call the information center at +1 575 472-3763 for details. More prosaically, it's just nice to look at.
There are several small wildlife refuges in the region that also provide breaks from driving, particularly during bird migration season. The largest smaller than the ones along the Rio Grande to the west, but still significant is Las Vegas National Wildlife Refuge east of Las Vegas, while the most convenient to the cross-country traveler is a small area at Lake Tucumcari, near the town of the same name along I-40. You'll also have chances to see wildlife as you drive here; the area east of I-25, for example, is rich in pronghorn antelope.
Another interesting thing to watch for as you drive is the remains of the historic Santa Fe Trail. The state of New Mexico has done a good job of erecting markers where the Trail crosses highways, with interpretive text in many locations, some of them photogenic. If you'd like a more up-close-and-personal experience with the Trail, start by visiting Fort Union National Monument, as listed under "Do."
Few of the towns of the region have much in the way of museums, etc., but there is a small museum in Raton with artifacts of 19th-century life. Open T-S during the summer, W-S the rest of the year; free. Clayton, Springer and Tucumcari also have small museums of primarily local interest.