Rather you are going on your honey moon, or just want a ramantic get away. I have found a great list of couples hotels for you to stay at. http://honeymoons.about.com/od/floridakeys/tp/FL_Keys_Hotels.htm
Yes, although I wouldn't think it's common, alligators can climb trees... Here's a picture: http://www.mallowandgogo.com/gallery/view_photo_properties.php?set_albumName=floridakeys&index=68&gallery_popup=true If there is a picture of a gator in a tree, then someone put it there. Alligators and crocs are not built for climbing trees. They are too ungainly, and their claws are not sharp enough to climb.