Capulin Volcano is located just off the highway between Clayton and Raton, NM. It's a near-perfect cindercone volcano. It's shape was preserved because lava flowed from a mouth (boca) near the base of the volcano. It's worth a drive to the visitor center, along with a rim-trail hike and a hike into the crater.
If you have the time, and especially if you're seeking state highpoints, consider driving the Dry Cimarron Scenic By Way into the Oklahoma panhandle. You'll have to bring a map to find this dirt road scenic by way. Once in Oklahoma you'll pass by Black Mesa, the highest point in that state.