The Mesa Verde- cliff dwellings scene has been suggested. Combine with a visit to the Navajo Nation and stay in their motel at Window Rock. Lots of interesting stuff in the area. Visit the Hopis (good food at their motel, but rooms a bit pricy), the Zuñis. The Anasazi ruins at Cañon de Chelly- hire a Navajo driver to get to the ruin CarolC showed. Monument Valley not too far, lots of rocks! Lots of driving, though! The country is warm but not too hot because of the elevation.
Or how about the Taos-Santa Fé area, the high road to Taos and the old Spanish villages and churches, and a good number of Indian pueblos close by to the west. The Valle Grande in the Jemez Mts., the most beautiful spot in New Mexico, just recently came under the Federal Government wing.
Or take a trip into Cajun country, the bayous and meet the people, and the Big Easy. Train travel is not the best way to see things outside of the major centers. The by-ways are the thing.
The Big Bend is a place to really see geology. Again, lots of driving. And be careful where you leave chocolate- the scorpions love it. And it is hot- did geology field work there one summer.
Mexico has much that is interesting, but not for the short haul, or the inexperienced unless you stick with a resort town in the mountains or on the coast.
Come for a week, stay for a year.