New New Mexican here (as in, I recently moved to New Mexico). I love this state. Santa Fe is a wonderful place, and the plaza is worth seeing, along with the New Mexico history museum, the galleries, restaurants, etc… Others have mentioned Meow Wolf, which is a must for a first-time visitor, at least if you’re into weird art. And if you’re on these forums, then you probably are.
Bandolier is really cool, too, and if you want nature, taking a trip further up into the Jemez Mountains and the Valle Caldera nature preserve is awesome. The hot springs up in Jemez Springs are less populated than you’ll find at the resorts down in Santa Fe. Unfortunately, the wild hot springs in the area aren’t as good as they used to be. There are some of those near Taos on the Rio Grande if you ask around. A trip to Taos is worth it, too.
And since you mentioned religious sites, most non-locals probably don’t know that right now, religious pilgrims are traveling across New Mexico, to sites like Chimayo, which is north of Santa Fe. Your Ultimate Guide to the Chimayo, NM Pilgrimage
Rancho de Chimayo is also an outstanding New Mexican restaurant. The Chimayo chile is a rare local cultivar that I love (more obscure than the standard New Mexico chiles). It’s a town that’s just rife with authentic New Mexican culture, even if less touristy and bougie than Santa Fe and Taos.
And wherever you are, ABQ, Santa Fe, and all points in-between, I can tell you were to go for the best New Mexican food, or just a good green chile cheeseburger.