Just a suggestion but you might want to post this last question as a topic all by itself. There are many here, Philippe immediately comes to mind, who know this side of the island well but who might miss your question buried in this particular thread.
I would suggest those 'off the beaten track' places, while lovely and well worth finding, should probably be discovered as a group effort rather than totally on your own.
One area that does immediately come to my mind is Loterie Farm and I understand there are guided hikes that will take you to the top of Pic du Paradis and this is a spot well worth seeing as the views from the top are truly spectacular - just not in a car these days from what I've read on various chatboards.
The other place that I've always found incredibly lovely is Fort Louis (I think that's the correct name...) at the top of the hill in the center of Marigot, easy to find and easy to get to and relatively safe as well, and again - spectacular views once there.
You have to be getting excited as your trip draws near. I hope it's a wonderful one in every way.