Albuquerque: 72 hours in
If you don't mind, may I ask where you live so I can tailor my recs a little better? ABQ has, for example, some fantastic Vietnamese restaurants, but I wouldn't send you to one if you lived in another Vietnamese-heavy area like LA or Dallas.
The stuff you'll almost certainly find to be unique would be the NM-style Mexican restaurants. The best ones tend to close very early (6:00 tops, many closing after lunch), a few perennial favorites are Mary & Tito's, Barela's, and Padilla's. If you want to have a margarita with your enchiladas, maybe best to drive 50 minutes north to Santa Fe and hit the Shed.
Green chile is NM's signature ingredient, and you'll find it on the majority of even non-NM-style restaurant menus, often used in creative ways. Giovanni's does a surprisingly good NY-style pizza with green chile on it, and Banh Mi Coda (a Vietnamese sandwich place) does a warm turnover stuffed with chicken pate and green chile. The green chile cheeseburger has become canonical here, served in an array of styles from fast food (try local chain Blake's) to fancypants (bar menu at Ranchers Club) and everything in between.
Hope this gets you started, happy to give some less region-specific suggestions too.