Have you considered cruises? This is just an example, but there is an MSC 7 day cruise starting and ending in Miami - November 23-November 30. It is an Italian line, so already you get a little foreign flavor. Port countries include Mexico, Cayman Islands, Jamaica and Bahamas. I never used to think cruises were for me, but I discovered they have so much variety that they can work for many different types of people.

You don't mention your land budget, but it is the other part of the package. And cruises can be quite inexpensive, including your room of course, but also all your food and a lot of your entertainment and transportation.

There a lots of good web sites for researching cruises, plus the cruise lines themselves have web sites. I find vacationstogo.com to be particularly functional for me. I did a "Custom Search, selecting just on a departures starting November 23 and being no longer than 7 nights. Lots of choices. On the site, the cruise I mention is #31666 .