The Vernal Regional Airport is the largest airport in the Northeastern Utah area. It is serviced by Boutique Air. They fly to Denver and Salt Lake and have 2 flights each direction each day. Check out their website for more information. The airport also serves small aircrafts that are privately owned and operated.
Other options would be the Salt Lake International Airport is Delta Air Lines’ second largest hubs, with over 350 flights departing daily. Several other airlines, including United Airlines, serve the airport. Salt Lake City is readily reached from anywhere in North America. From there, Vernal is just a quick trip.
Or the Walker Field Airport in Grand Junction, two hours from Dinosaur National Monument. The airport is the largest in western Colorado and connects to all major hubs in the United States.