Ah, while New Mexico is not as large as California, it is the nation's fifth largest. And the towns and attractions you mention are, in a couple of cases, at opposite ends of the state.
My recommendation is that you restrict your travel to one region within the state. Say, north-central, which offers a LOT to see and do, and is at somewhat higher elevation, so less summer heat.
Pay a visit to NewMexico.org, the tourism website. You can choose a destination region to learn more. These two are the ones for north-central and central:
https://www.newmexico.org/places-to-go/regions-cities/northcentral/https://www.newmexico.org/places-to-go/regions-cities/central/Lynn