United has round-trip flights from Dallas (DFW) to Bahamas, Grand Cayman, Costa Rica, or Belize (NAS, GCM, SJO, LIR, BZE) for $255-$337 with a connection. See the list of example dates (middle of the website post) for details on which months are available for each destination. Very few weekends available. Origin/Destination reversible.
Note: Nassau is the cheapest at $255, Grand Cayman is the most expensive at $330-ish. All other destinations are about $290.
United’s “Basic Economy” fares do not allow for a free carry-on bag. Only a personal item (like a small laptop bag) is free. Seats are randomly assigned for free prior to boarding. If you have the United Explorer credit-card, use the “free checked bag” perk.
The personal item size on United is smaller (9 x 10 x 17 inches) than Frontier or Spirit (8 x 13 x 18 inches).