Is it safe to visit Cozumel, Mexico?

Cozumel is in the Mexican State of Quintana Roo, which is a popular tourist destination known for its beautiful beaches, coral reefs, and vibrant culture. While no place is completely without risk, Cozumel is generally considered safe for tourists. Cozumel has a lower crime rate compared to other parts of Mexico, and it is a popular cruise ship destination, which means that the local authorities are accustomed to handling large numbers of visitors.

What the State Department Says...

The U.S. Department of State has issued travel advisories for Mexico, including the State of Quintana Roo.

Exercise increased caution due to crime.

Criminal activity and violence may occur in any location, at any time, including in popular tourist destinations. While 
not directed at tourists, shootings between rival gangs have injured and killed innocent bystanders, including U.S. 
citizens. Violent crime, including homicides and assaults, has increased in Tulum.

There are no restrictions on travel for U.S. government employees in Quintana Roo state. Exercise increased caution 
after dark in Cancun, Playa del Carmen, and Tulum and remain in well-lit pedestrian streets and tourist zones.

I do note that these advisories do not mention Cozumel specifically, and the crime they mention is primarily on the mainland. There are no travel advisories for Cozumel itself.