Cozumel is a Caribbean island just off the Yucatán Peninsula in southeastern Mexico. It has great diving, nice people, safe streets, and prices comparable to other Mexican tourist destinations. The diving is the main draw to Cozumel; if you prefer white sandy beaches then other nearby destinations would be a better bet (e.g., Playa del Carmen, Tulum, Isla Mujeres.) It was badly battered in 2005 by Hurricane Wilma, but, with few exceptions, has been completely repaired.
Alternatively, you can fly into Cancún (CUN IATA) which generally has more flights, then take a bus or van south to Playa del Carmen and take the ferry across to Cozumel. A shared van from Cancun airport to Playa Del Carmen will cost around M$300 (pesos) per person one-way, where a bus will be around M$130 (or equivalent US dollars if you do not have pesos handy) per person one-way.
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