Some options:
Cancun is 5-6 hrs. each way thru Houston.
Cozumel is 7hrs. thru Denver on Frontier - if you're coming back here afterward, the return is to a regional airport SE of Phoenix - Williams Gateway (AZA) - about a 30 min. ride to downtown in traffic. Otherwise it's 18 hrs. back thru Denver.
Some of the Caribbean is possible - look at places USAirways serves since we're a hub city.
We can get to Provo (Turks/Caicos) in 8hrs thru Charlotte - there's also one 8hr AA flight thru Dallas - Sat only.
Curacao is 8hrs. via MIA but the flight arrives at 8:15PM.
St. Croix is also possible in 8hrs. with a 9PM arrival - one flight only, the rest are multiple connections.
Grand Cayman also but it's either a 2AM departure or an 8:30PM arrival. - relatively inexpensive though $582 r/t.
Roatan is 6+hrs. thru Houston on United. 5:30AM departure puts you there at 12:45PM. We've done it twice recently. You can continue on to Utila via the ferries arriving on Utila at 5PM. Long day but it's broken up by about 2 hrs. on Roatan plus 2 ferry rides.
Belize on United thru Houston is 5-7 hrs if you're willing to pay a little more.
Everyone one of these ^ options are 1 stop with typical layover times.
The only non-stops I'm familiar with from here are to Hawaii.
Maui, Honolulu, Kona or Kauai are direct. Honolulu is $500 r/t, the others $650. The return back from Kona is an all night flight.
Check all your options here:
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