If you want to do some national park sight-seeing during the drive I would fly into Vegas and fly out of Denver (or vice versa) if you can swing it. Driving to Moab you have Zion, Bryce Canyon, Capitol Reef, and Canyonlands National Parks. On the way to Denver you'll have... well... pretty much the best of what Colorado has to offer at your disposal (you'll have to pick and choose cause no way you can it all).
If flying into and out of two seperate airports is not an option, I would probably pick Denver over Vegas. The drive from Denver to Moab will be a lot more entertaining overall, and in my personal opinion is Denver International is one of the less-annoying airports in country.
If you are looking to just drive in and out in the most efficient way possible... Salt Lake City.
If you want to go full tourist mode... flying into Sunport (Albuquerque International) is another option. Telluride is of course a big tourist hot-spot, Durango has the Durango/Silverton Narrow-gauge Railroad (awesome), Pagosa Springs has some awesome hot springs available, and there is Los Alamos National Labs if you are into World War 2 history. And of course you will be close to all of the major indian reservations if you want to explore some of their culture/jewelry/etc. All of that is along the way between Moab and Albuquerque.
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In terms of airlines...
- Denver - Southwest/United
- Albuquerque - Southwest
- Vegas - Southwest
- Salt Lake City - Delta