Kerr, a big Cruisemate welcome! You certainly picked a beauty of a ship, for your first cruise, good for you.
Your beach day in Labadee could end up being the highlight of your crusie, as it is for many. This port has been redone, and, upgraded,with tons of fun things on land, plus wondeful water fun! Local arts and crafts are offered for sale by the locals
Falmouth is a rather new port,and experiencing some growing pains, with mixed reviews. The locals in Jamaica, can be a "tad" aggressive, and that puts many cruisers off, so be forwarned..Taking a ships tour if offerred, may be the way to go in this port.