There are plenty of options;
Cancun (or Mexico) with Aeromexico, daily.
Panama City with Copa, daily.
Grand Cayman with Cayman Airways, not every day.
BahamasAir from Nassau is doable but they have only a few flights a week and may be difficult with the connections unless you want to stay in Nassau.
Lacsa (Taca) has a weekly(?) flight from San Jose, Costa Rica.
Nassau and Santo Domingo (Dominican rep.) is also doable if you don't mind flying Cubana. Cubana does these flights a few times a week so similar problems to BahamasAir.
I think the choice depends where else you want to travel and if the non-daily options work for you. The flights from Grand Cayman are probably the easiers for caribbean but if you include central america, both Cancun and Panama are very easy and convenient as well.