The best option is to exchange at a bank in the U.S (not at the airport) prior to traveling. The second-best option, which is generally what we do, is go to the grocery store called Mega, and use the ATM. The ATM fee is around 3 USD, and the exchange rate is the same as the banks. Most hotels will also have an ATM, but the fees may be higher.
Almost all places on the island accept credit cards, with the exception of a few smaller shops and restaurants. In most cases, they will accept US Dollars if you do not have Pesos. We usually like to have Pesos on hand just in case, but it is not a necessity.
Drinking tap water in Mexico is NOT RECOMMENDED. All restaurants and bars provide either filtered or bottled water to drink. It is recommended to bring a re-usable water bottle. You will find filtered water dispensers in almost all hotels or rental homes, and again, bottled water is available any place that does not have a filtered water dispensing system.
Taxis are available everywhere on the island and are reasonably priced. A rental car is a convenient option and there are plenty of available rental car agencies at the airport or on the island, but it is not required to be able to get around easily.
La Monina, Bajau Steakhouse, Coconuts (cash only), Cozumel Dreaming Sushi, La Choza, Portosol, Coco Cafe, Banana & Co, Los Sera's Tacos, Mister Taco, Corazon Contento.