OK - then go to the US Virgin Islands. Jamaica is nice, we have been there 3 times, but the off-resort stuff is kind of not nice. Not as bad as Mexico, but still pretty nasty.
We loved St. Thomas when we were there. We went off the resort all the time, and it was great. Took a ferry to St. John which was AMAZING and went on some very nice tours. We also took a kayak tour of a mangrove lagoon and it was wonderful.
I don't remember the name of the place we stayed for our honeymoon in St. Thomas, but it was nice.