Honeymooning in October on a Budget?

Hello everyone, and I appreciate your time in helping my wife and I with this decision.

Leaving from Florida.

TL;DR – Our budget is hopefully $3000 and we were looking for something in the Caribbean. October 16-22.

Mainly we are looking for something to just relax, but some activities would be nice.

I'm the type that if we didn't have an all inclusive I'd be worried about money the entire time, but all inclusive have proven (so far) to be quite expensive for literally anywhere.

Originally we wanted to go to Barbados since I used to live there when I was a wee one and would love to visit again, see the Rum Distilleries etc, but the flights are very expensive as is the price per day (according to other sites)

Then we thought about Puerto Rico because it was one of the cheaper options, the flight and hotel were great options until we realized it wasn't all inclusive, and didn't know the prices to expect each day for three meals, drinking, etc.

She doesn't like the idea of a cruise since it seems that they don't give you a lot of time to explore and stuff, but I told her we have an entire day on certain islands, and she's slowly warming up to the idea

Is there ANYTHING in our budget? Or are we thinking ridiculously?