Zachary Taylor State Park is a great semi private beach that is a great way to relax on a budget. It costs $2.50US to walk into the park. It's about a mile and half from the pier to the beach, and it is a beautiful, easy walk. There are changing rooms, Bar/restaurant, Hammocks, and the old fort is cool to poke around.
We arrived in port and were off the ship around 8am local time to beat the crowds on what we knew was going to be a very crowded day at Chankanaab. We quickly exited the International Pier Complex, grabbed an official taxi from the stand at the pier, and for $11USD the four of us were on the way to Chankanaab! It was $21USD per adult and was totally worth it. We made no reservations and just went for it. It saved us a lot of money going it on our own. While in the park we hopped on to a guided tour with an awesome guide Felipe, who explained all of the Mayan culture and history. The Tequila tasting was great. For $7USD you can get a very strong margarita served in a souvenir clay cup which was cool. The Sea Lion show was fun! We brought our own snorkels, and the snorkeling right from the beach was much better than I anticipated. Amazing day on a budget in Cozumel. Avoided feeling restricted to a ship excursion. Freedom in paradise!