We stay at Oasis RV Park in Amarillo and Santa Fe Skies RV Park in Santa Fe each time we are in those cities. Santa Rosa State Park has paved W/E campsites and a dump for $14/night, which includes the park day pass. We have also stayed in Sayre, Oklahoma, at the city park campground. Long, gravel, W/E pull-thrus and a dump for $12/night, plus public swimming pool, golf course, ball fields, tennis courts, playground, and picnic area built by the CCC in the '30s. The nicest casino campground in New Mexico is at the Isleta Pueblo on I-25 just south of Albuquerque--golf course, fishing ponds, backs up to the Rio Grande, shuttle to the casino, FHU campsites. Take a look at RVParkReviews.com for other campers' opinions of these locations.
Flying J truck stops have RV fuel lanes separate from the truck lanes, overnight RV parking spaces, RV dumps, water, and generally propane. We like the ones that also have a Denny's so we don't have to fix dinner or breakfast during a "sleep stop". We spent a night at the Flying J on the west side of Albuquerque on I-40--noisy, but free. But that's why we have good ear plugs!
Enjoy your trip!