I graduated from Fort Lewis College in Durango - a long time ago. I was in their third graduating class back in 1966. I grew up in Farmington - fifty miles south of Durango. I have lived and visited the area off and on, but have lived in Georgia for over twenty years.
Disclaimers out of the way - here are my thoughts. At the Four Corners are vendors selling various foods and trinkets. Plan to be hungry enough to get a Navajo taco. If you aren't very hungry - plan on splitting it three or four ways. They are very large. Navajo tacos may also be found throughout the reservation communities. The best I ever had was in Tuba City, but I understand that that particular restaurant has recently closed.
Several posts on some message board suggest that there is very good BBQ in Moab. I don't recall the name, but I doubt there is more than one BBQ place in Moab. Locals will know what and where it is.
Silverton - fifty miles north of Durango - has a year round population of less than 500 souls. Last summer they had twenty restaurants - mostly selling lunch to the tourists who rode the train up from Durango. The best places in Silverton vary from year to year - but one or two are usually pretty decent. If you have time, I would suggest you ride the train from Durango to Silverton and return on the bus. Reservations are necessary. The bus ride back allows you to return to Durango sooner and to see a bit more of the area.
Farmington has a brew pub at the corner of Orchard and Main. That should be something like 101 E Main St. It is in an old turn of the century drug store building. It has opened since I was last in the area, but it gets high marks for both their brews and their food from what I have read.
Green chile cheeseburgers are popular throughout the New Mexico area. Blake's Lotta Burger is one of the better sources.
The last time we were in Cuba (midway between Farmington and Albuquerque) we had the best meal I have ever had in Cuba - and I have been visiting Cuba since 1951. I don't recall the name, but it is in a southwestern looking building on the right side (when northbound) after you have passed through most of the community.
I know that I am being vague, and I apologize for that. Just the same, I hope this and the other posts help you to have a most enjoyable visit. Please let us hear about your trip when you return.