We've made that trip numerous times. We just got back from skiing in Taos, NM. Other trips were through NM, the Grand Canyon, Yellowstone, Yosemite, California, etc. I start with this website first. Once I get an idea of the route and area, I use:
RV Park Reviews - Trusted Reviews of Campgrounds & RV Parks
rvparkreviews has info about most parks across the US. I've found most reviews pretty accurate. Parks range from deep boonies, national and state parks and parks in the concrete jungle of the New York City area. You may not find every answer but it's a good place to start.
We were tent campers forever. That ended about 10+ years ago. We went from a travel trailer, two 5th wheels, now we move around in a motorhome. Our very first trip in our TT rving was to NM from Texas. We stayed in Albuquerque, Santa Fe, Demming, Alto, then back down through Carlsbad. All planned through the RV Park Reviews Website.
2015 Georgetown Forest River 351DS MH
2008 Keystone Cougar 293SAB 5th Wheel
2007 Jay Flight 30.5RLS 5th Wheel
2006 Jay Flight 29BHS TT