One of the best things about Cozumel is how many iguanas will pose nicely for you, especially in Chankunaab National Park. If you don't want to go on an organized shore excursion, take a taxi to Chankunaab, one of the island's highlights, where you can mix and mingle with visitors, locals, see shows, snorkel, take a cultural walk and, yes, hobnob with handsome iguanas.