The Palace Hotel, downtown, is a good place to stay.
Pinos Altosat 9km
Route 15at 25km
This is a beautiful road but is quite narrow by US standards. Can sometimes be closed due to snow in the winter. Spring and Fall are the best times although, due to the elevation, it's much cooler in the summer than the surrounding area.
Gila Hot Springsat 61km
Gila Cliff Dwellingsat 67km
This National Park allows you to walk up and through ancient cliff dwellings.