DFW non-stops to the Caribbean: Cayman Isl, T&C, Aruba, St Lucia, BVI, San Juan, Jamaica, St Martin, Roatan, Cancun, Cozumel, Belize, Honduras, Nassau. Direct flights from Dallas-Fort Worth (DFW) - FlightConnectionsThere are not direct flights from Dallas though, they all go through Miami last I checked but I will dig into that here in a bit.
For prices, beaches, and non-divers, how about Cancun, Aruba, or Montego Bay?