want to try to explore the islands on our own
Cayman and Cozumel are good places to do that.
San Gervasio ruins in Cozumel - any tips or experiences
You should put ruins in quotes. They are the San Gervasio "ruins". They are to Mayan Ruins what a single-wide in the boonies is to a luxury home. ...if the single-wide charged admission. It's like Hell on Cayman: overhyped tourist trap that everyone needs to see once just to say you got suckered.
But it's easy enough to get to. You can see it on any mapping software - straight east from San Miguel, take a left at the sign, go between 4 and 20 miles through the low scrub of Coz until you get to the park entrance. All the cabbies know where it is. In twenty minutes when you're done looking you can hit the gift shop which has far more to see, and then head back to town.
When on Coz don't forget to buy vanilla. Los Cincos Soles - plastic bottles. $15 for a liter.
On Coz you can eat American food at any of the chain party bars near the pier(s) and a few fast food joints around, you can get American-style Mexican food [Tex-Mex] at Las Palmas or Pancho's Backyard, more authentic Mexican at Viva Mexico's cantina [upstairs, menu prices are in Pesos, don't have a coronary; just divide by 10], and really authentic Mexican back a few blocks in any number of store front cantinas with two tables and five chairs and virtually no waiting.
SIG: If you're going to create the drama, at least supply the popcorn.