Cliff's Amusement Park is probably the most well known to coaster enthusiasts - located in Albuquerque proper, it is a compact and landlocked park surrounded by commercial real estate. One of Custom Coasters' later wood rides, The New Mexico Rattler, serves as the premier attraction. Interestingly, it is actually Western Playland in the Las Cruces/El Paso suburb of Sunland Park that contains the highest number of coasters and acreage in the state. The park actually moved to its current location in 2006 when it was lured over the border from Texas by the Sunland Park Racetrack and Casino, taking most of its largest rides with it. Outside of the collected production model coasters (El Bandito, a extra large Z64 Zyclon being the rarest), the park contains Larson Flying Scooters, a skyride, and several other attractions.
Interestingly, while many people associate New Mexico with "desert", there is very little in terms of water parks there. Cliff's has a few slides, and the City of Carlsbad has a municipal aquatics facility that opened in 2016. However, that's about it. Surprising, I know. "Dry slides" are about as common - Red River Ski Area has summer tubing runs to go with its multi-person and single person ziplines.
Trains and carousels operate in smaller parks, just as they do elsewhere in the nation. Spring River Park and Zoo in Roswell features both along with a collection of animal exhibits. Meanwhile, the Toy Train Depot in Alamogordo has a couple of different narrow gauge tracks that humans can ride as part of their overall exhibition.
The state has some living museums as well, providing people with a glimpse into history. Both the Aztec Museum and Pioneer Village and Sacramento Mountain Museum & Pioneer Village go into the past and pull out costumes and buildings to try and bring back that homesteader feel.
Finally, there's the Meow Wolf Collaborative piece known as the House of Eternal Return. Its part art installation, part fun house, all original, and a Themed Entertainment Award winner attraction. Only City Museum in St. Louis is comparable.