We have done Coz many times. We have done the excursions from the ship and on our own. Coz is fairly easy to navigate on your own.
To answer your questions:
I understand that there is a lot of shopping downtown, which is just at the other end of the dock.
The real shopping is in town but not necessarily on the maps the ships shopping guide gives everyone.
Are there beaches nearby where you can go to just relax and soak up the sun?
Yes, lots. Many have package deals, some have only an admission fee, and some are free.
If we decide to take a taxi to one of the parks, do the taxi drivers take US currency or will we need pesos?
The locals will almost always take USD, just be sure you know the exact amount and have lost of small bills so as not to need change back. Simply moving the decimal point on their prices is close. Negotiate ! Bargain!
How safe is it to explore on one's own?
Just don't wander too far off into neighborhoods. There are alot of hidden shops etc "underground" that many never get to see by sticking to the main drag.
We have used the maps from these folks. They are really nice folks and have great maps. Below is the update from them and the link to their stuff.
Can-Do Cozumel is the map you want. We already ordered ours.
The much awaited Isla Mujeres and Cozumel maps are at the printer now. We have been told that as long as there are no printing complications we will have maps to mail out to you by Wednesday, May 6th.
Both of the maps are now available for pre-order on our online store.
If you need a map fast, I recommend ordering Priority shipping, I plan to
get every order filled the same day I get the maps, but I will fill the
Priority requests first.
Thank you so much for your patience, we hope you enjoy the new maps!
safe travels, Perry & Laura"
Hope all this helps. We have a gallery on the Ecstasy/Fantasy sailings at
Phil & Liz