When we had one toddler, and then eventually a toddler and an older kid, we always found a way to make a one-bedroom suite work.
Kid usually went to sleep first: we'd get her to sleep in the King sized bed while we stayed up later in the living room or on the balcony. Then, when it was our bedtime, we'd get the sofabed ready, turn out all the lights, and I'd quickly relocate the sleeping beauty to the sofabed, usually without a peep. Then we'd go into the bedroom, close the door, and get ready for bed ourselves.
Worked for many trips in Residence Inns, MVCIs, Marriott Suites...and even the occasional Embassy or Homewood when we were doing Hilton. If you can make a 1BR work, your options open up greatly. Then you can pick almost any kind of destination - city, beach, etc. - and find something.
That said, if your #1 pick is really the Caribbean, I've always heard good things about the St. Kitt's property. It seems to regularly make villas available to award users, which is refreshing given that so many MVCI's don't.