Cozumel's free list is unusually strong, and the reason is legal as much as geographic. Under Mexican law the shoreline is federal public land, so there is no such thing as a private beach on this island — what looks like an exclusive stretch in front of a resort is public up to the tide line, and what beach clubs sell you is the chair, the buffet and the pool, not the sand. Add to that a reef that comes close enough to shore to swim to, and a town that puts on a genuinely local evening in its main square, and a visitor with no budget at all can have a real day here.
The catch is that Cozumel's cost model sits in an unfamiliar place. Most of the good west-coast snorkelling spots charge no entry and run on a consumption minimum instead: you buy lunch and a couple of drinks, and the chairs, the showers and the steps into the reef are yours. Money Bar at Dzul-Ha, Playa Corona and Sky Reef all work this way. That is excellent value and it is not free, and the difference matters if you are planning a day around twenty dollars.
The second catch is transport. Nothing on this island is far, but there is no visitor bus network and no reliable rideshare, so getting to a free beach costs a fixed-zone taxi fare: roughly $25 each way to Playa Palancar from the southern piers, mid-teens to the nearer west-coast spots, more again to the east. A genuinely free day therefore starts either downtown, where you can walk, or with a group splitting one taxi four ways.
What is properly, entirely free: the malecón and the waterfront along Avenida Rafael E. Melgar. The main square and the church beside it, and the Sunday evening when families, music and food stalls fill the plaza. Every beach on the east coast, including the natural limestone arch at El Mirador, the sand at Playa Bonita and Punta Morena, and the ironshore between them. The sand at Playa Palancar. The market streets three or four blocks inland, where you can eat for a fraction of pier pricing. And the sunset, every evening, over twelve miles of channel with the Yucatán mainland dark on the horizon — a west-facing island sunset that most Caribbean destinations cannot offer at all.
One thing that is not free and is frequently assumed to be: the marine park fee. Roughly $13 per person per day applies to boat entry into the Parque Nacional Arrecifes de Cozumel for diving or snorkelling. Swimming and snorkelling from the shore at a beach bar is normally covered by what you spend there, but if a boat is involved, so is the fee.