I travel so many different places that I have a hard time keeping up. Ergo, I opt for Skype and even have a Skype in number so peeps can always call me when I'm out of coutry.
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Almost everyone in Cozumel uses WhatsApp, which will allow you to send messages and make voice calls over a data connection (such as wifi) for free. Just grab the app and set it up before you leave home.
Call ATT and unlock your phone. Buy a SIM card when you're there. Insert SIM card. Problem solved.
This is a no brainer.
In Coz, I had more difficulty buying a SIM card than I have in most places. As far as I could determine using my mediocre Spanish, the convenience stores don't sell them--they could sell me additional time, I believe, but not the SIM card itself.