Looking at wind maps for the Caribbean in the winter months, over a period of weeks the southern Caribbean has the most reliable trade winds. No where is ALWAYS windy, but cold fronts coming down from the north regularly disrupt the trades further north (Cuba, the Dominican, Puerto Rico etc.) & have less effect further south in the Windward Islands (St. Lucia, St. Vincent, Grenada, Barbados etc.). The wind is also generally more reliable in the Leeward Antilles (Aruba, Margarita etc.).
The Colombian coast north of Cartagena might be the most consistently windy spot in the Caribbean in Jan/Feb/Mar. I just returned from 4 weeks in Santa Veronica, Colombia (about 1 hour north of Cartagena). The wind about 20 or 30 miles offshore was consistently 30-40 knots for days on end. Near shore that translated into 20 knots + most of the time, peaking at 25 - 30 knots. Further north along the coast is Cabo De La Vela on the Guajira peninsula. It's still windier & a flat water spot. Very remote & not really a spot for "nightlife" however!