There are no beaches in or near Belize City, which is where you anchor. For those the best thing to do is go to one of the barrier islands like Caulker Caye. There are other cayes too. These can be reached by water taxi fairly quickly. One can find these tours for sale at the pier. Belize is one place where you might want to consider the ship's tours because it is a tender port and if you are on a ship's tour you will get priority for the tender ride ashore.
As Penny mentioned, you can't go wrong with Chankanaab or Paradise beach at Cozumel. I also recommend Playa Mia and Mr. Sanchos. All of these can be done just by getting a cab at the pier and telling them where you want to go. All of them have taxis waiting for the trip back so you have no worries about being stranded. You can buy admission at the entrance, although some have no entry fee - they just expect you to buy X dollars worth of food and drinks. Look here
for more details on Cozumel beaches.