I never stay on the ship 100%. I will at least get off, walk around for 30 minutes to an hour, and get back on. Doesn't matter if it's a stop I've been to 4 times in the last year, I enjoy getting off the ship for at least a little bit. My wife and I very rarely do ship-organized excursions unless we win one onboard or are traveling with family/friends. Typically we will get off and do our own thing.
My last cruise we went to Bimini and if there ever was a stop where I would be tempted to just stay on the entire day, that's the one. Just not much going on the island unless you want to ride the tram over to the casino from what I could see.