You will have a wonderful time on Explorer - She is a fabulous ship with plenty of nightlife. Wandering from one spot to the next along the promenade will keep you busy. The Chamber is an awesome disco and gets quite busy after 11.
As for ports - Labadee is RCI private island so it is really just a beach day. If this is your first time in Ocho Rios I would suggest you do Dunns River Falls. My favorite things to do in Cozumel are to go snorkeling and make a required stop at Carlos and Charlies.