Southern Utah gives you a huge bang for buck. And you can spread a little further to add fantastic stuff in surrounding states. I'm not American but have flown from Australia several times to hike in Utah and its neighbours.

In 10-14 days, you can do an exceptional loop from Las Vegas taking in:

  Bryce Canyon NP
  Byway 12
  Capitol Reef NP
  Goblin Valley
  Dead Horse Point SP
  Arches NP
  Canyonlands NP
  Goosenecks SP
  Horseshoe Bend
  Antelope Canyon
  Zion NP
  Valley of Fire SP

Then when you go back, you can do places requiring a bit more planning like Coyote Gulch (amazing), Buckskin Gulch (also amazing), and secondary spots like Natural Bridges, SR 95, etc. Hundreds of great places in Arizona, New Mexico, Nevada, etc, and all before you get to adding anything more remote or long distance.