^ those places are as safe as anywhere.
Random shit happens everywhere, but tourists are safe & generally off limits -- that's how the gangs/thugs make their living, they have no real interest in disrupting that. Of course, if you're in a Mexican nightclub off premises at 3am, then...
To answer Chad's question, again -- it really makes no difference what island/country you choose if you're doing the AI style vacation. My advice, per usual, is that with All Inclusive Resorts, you really do get what you pay for. Particularly in terms of food, drink, and most importantly the clientele you'll be spending your vacation with ...they are not all created equal, or even close.
Mexico and DR offer the most choices in terms of the Luxury AI resorts & flights are plentiful & cheap compared to the smaller islands. CVG has direct flights to Mexico, DR, and Jamaica.
Aruba, while by far my favorite island, has nothing in that genre.