Moab's restaurant scene is better than a small desert town has any right to be, driven by the steady flow of well-heeled outdoor tourists with appetites built up from a day of hiking or biking. The main strip on N. Main Street has most of the options.
Desert Bistro on East 100 North is the best restaurant in Moab — a proper sit-down place serving creative American cooking with local and regional ingredients in a historic adobe building. It is relatively expensive by local standards and worth every cent. Book ahead in spring.
Pasta Jay's on N. Main is a long-running casual favourite for pasta and Italian-ish food at reasonable prices. It fills up early in the evening.
Moab Brewery on N. Main is the obvious choice for lunch after a morning in the parks — a brewpub with reliable burgers, sandwiches, and good beer brewed on the premises. The patio is pleasant in the evening.
Peace Tree Juice Cafe on N. Main is a good option for breakfast or post-hike recovery: sandwiches, smoothies, salads, and coffee. Popular with the outdoor community.
Note that Utah's liquor laws have historically been restrictive — most bars require "membership" or operate as licensed restaurants. This is much less of a barrier than it used to be, but worth knowing if you want drinks with your meal.