hey, Leigh! 4 nights in mexico?
would south of cancun interest you? the riviera maya has awesome resort that are nothing like cancun--cheap car rental for $20-25/day and the mid-range all-inclusives are well under $100/person for early june. try interlinetravel.com (no fees outside of 4 days booking)
delta service is good for places like LIR (Liberia Costa Rica) so if you want to splurge a little more, Occidental GRAND Papagayo is very deluxe--prices vary but it IS premier property in the area.
Islands are tougher with the schedules--daily service via ATL vary so much--some are wkly, some more sporadic, but also have service thru NY. Dominican Republic is not a bad choice for June--BUT--the resorts go from great to just so-so in price and amenities.
We liked the idea of Cabo until we went--most beaches are not swimmable, but if you like pools, the mountain/beach aspect is interesting. Haven't been back since! They really want you to pay for upgrades to ocean view rooms--so many are garden (that means parking lot frequently) so be aware.
Antigua might be good chocie--if you can get the Verandah for a song--might be possible--thru interline agency.
I have no good feelings about western carib at all--not my cup of tea whatsoever. outside costs are exorbitant.
Just my 2 cents worth--I've been to lots of AI's--air access/tourist taxes and extra costs are factors to consider.
Good luck--keep checking back here--you'll get lots of ideas.