I live in Cortez. Tequila's is the best mexican; Mama Ree's and Nero's for Italian; Shiloh for steaks, Main Street Brewery for good all around food and try their "schnoozerboomer" brew YUM and I don't like beer.; Homesteader's is good for Lunch. In nearby Dolores, try Old Germany. Ddurango has some really spectacular food as does Telluride. Let me know if you want places there.
Just back from Mesa Verde and Santa Fe. In Cortez, FINE dining to be found at the Far View Lodge inside Mesa Verde Nat'l Park. Don't miss this one!
In Cortez we found a good mexican food place (Tequila's, I think,) and there is a great brewpub on Main Street - they grind their own beef, good beer, and a knockout home-brewed root beer!