Ashley, I agree with Shelley - definitely go Cave Tubing in Belize.
Although it is definitely cheaper to go it alone - as Shelley also said - be very aware of your time. If you are on a ship's excursion and they are running late (for whatever reason) the cruise line will take responsibility for getting you back onboard. If you make your own arrangements, they assume NO responsibility.
There are numerous suggestions for excusions and reviews of each of these ports at our sister site www.PortReviews.com
. In particular there is a very good special report on the beaches in Cozumel.
Follow this link: http://www.caribbeanportreviews.com
and click on each individual port for more info.