If museums are on your list of things to see, you might want to browse the collections at Aztec Mill Museum in Cimarron Historic District. If you want to see more of the museums in Cimarron, National Scouting Museum isn't far either.
Cimarron Canyon Wildlife Area is 5 mi (8 km) from central Eagle Nest, why not stop by during your stay. Want to stretch your legs some more? Head to Enchanted Eagle Park, located nearby.