Barbados is probably your best bet ... generally decent award availability in Summer, best infrastructure, minimal crime, some tourist sights outside the resorts (albeit nothing mindblowing), plenty of good restaurants outside the resorts, outside the main hurricane zone and not been hit since the Queen took the throne!

But still fundamentally dull compared to the Miami trip you outlined. However, that's the sort of thing I did before I had kids, and now I've got two I am quite happy - especially at their young age - to stick them in the kids club (where, after 2 days, they INSIST on going to rather than being with us) and sit on the beach and in the pool.