I'm an avid caribbean traveler, scuba diver, and backpacker.
I THOROUGHLY enjoy St. Martin (french side) and Tortola. I am NOT a fan of "Las Vegas with a beach", so I avoid Cancun, parts of the Dominican Republic, Grand Cayman, etc.
If you want to get away from everyone, here are a few of my recommendations -- and I've found hurricane season to be the BEST time to go, hardly anyone around and 95% of the time you get AMAZING weather
1. Treasure Cay, Bahamas - Treasure Cay Resort; Green Turtle Cay; Hope Town (Elbow Cay, although easier to reach by Marsh Harbour). No mega resorts, very friendly staff, all willing to give you deals during off season. Easily reachable via Nassau, and to some extent Florida
2. Tortola - wow, amazing. Long Bay Beach is one of the most photographed spots in the Caribbean. LBB
Resort is very well self contained.
3. St. Martin - we stayed at the Radisson and was VERY impressed. We had a lot of fun at Grand Case. The Dutch side is just VERY VERY busy, but reachable by boat or cab - so you can easily "escape" the McDonalds/Hard Rock type atmosphere. Maho Beach before flying out is also a must, and is only a 10 minute walk back to the terminal. Drinks are a bit pricy though @ the bar.
4. Belize. simply amazing. they speak english and take the USD 1 for 2 BZD.. easy conversion.
5. T & Cs - same as the Bahamas -- you'll be able to negotiate prices down a bit, enjoy some amazing diving, and avoid the "Vegas with a beach" scene.