Catch some winter-league béisbol
You’d be hard-pressed to find a major-league roster without at least one player from the Dominican Republic, and winter-league games here often feature future or current major-leaguers getting some ABs in the off-season. Dominicans are passionate about baseball like the rest of Latin America is about soccer, and a game in Santo Domingo or San Pedro de Macoris isn't just a way to see MLB talent on the cheap; it's a way to experience this country's own special take on something quintessentially American.
Surf the most underrated spot in the hemisphere
Put everything you thought you knew about Haiti aside for a second. It is, by most accounts, the best surfing country in the Caribbean. In the south, hit the Bay of Jacmel and Pistons Beach for the best-known breaks in the country. If a cold front is coming through, head up north to La Pointe, Ginsu, and Caracol.