Cozumel and Bahama's tips

My family and I are going on our first cruise this July and will be stopping at Cozumel for one day and Nassau for another. Are there any good spots people can recommend for those days with such a short stop?

I'd like to do some easy diving in either or both places.

I've never been to Nassau, so I can't comment on that. However, there are a variety of dive operators near the docks where the cruise ships come in in Cozumel. Lots of good sites close by. Be aware that most of the diving in Cozumel are drift dives, which have their pluses and minuses. They are very easy dives, as long as you aren't trying to stop and take photos, then it becomes a bit more work to stay steady. I stayed at a resort down the coast, so I am afraid that I can't offer any advice regarding specific dive operations (also, my sister-in-law handled all the dive coordination). Have fun, the water is generally extremely clear there with great vis.