I found some copied info on the best and largest mayan site on Cozumel Island. This might help, but its not coming from first hand knowledge though. Hope someone else can give that to you.
The Mayan archeological site of San Gervasio . Located on Cozumel Island is a good choice. It is located in the heart of the island, in a lush jungle populated with brilliantly colored iguanas. So one can see why no one ever wanted to abandon this beautiful place back in the 16th century.
San Gervasio was a site dedicated to the Mayan goddess Ixchel. A graceful arch protects an altar on a sacbe (ancient road) leading into the ceremonial center. Many statues to Ixchel were found here. It is believed that a large ceramic image of Ixchel delivered oracles spoken by a hidden priestess for pilgrims with questions.
Although the ruins at San Gervasio are not well preserved, they are numerous and their beautiful natural setting makes a visit there worthwhile. One of the most interesting buildings there is the Temple of the Hands. Inside, numerous small red hand prints of unknown significance are painted on the wall, leading more than one tourist to speculate that perhaps this was a day-care center for pilgrim moms!
Cozumel is a very important historical site for the Mayans. One can easily spend hours exploring the interesting ruins located on this fertile jungle island.
Hope this helps a little bit. I know there are two others, but you can only get to one by jeep, and the other is smaller and not as imressive.
P.S. I dont know about the safety factor around the island, but I felt safe nomatter where I went. It could be a little different for women though...