An article in USAToday points out several new routes to the Caribbean, including the DR, St. Lucia, and Barbados:
Cheap flights to the Dominican Republic won't be hard to find this summer thanks to ultra-low-cost carrier Spirit. The airline has recently resumed its service between its Ft. Lauderdale hub and Punta Cana, Dominican Republic, available through September 8. Meanwhile, Spirit's new service to Santiago from Ft. Lauderdale begins June 20.