Every time we go to Cozumel we find something new (only 14 trips so far).
Here are two addtions to Christi's list that I have not found mentioned elsewhere:
La Lobsteria-Calle 7 Sur at Av 5--This is a really good place; recommended to us by Jamie, our maitre d' at Casa Mexicana. Our group of 10 arrive unexpectedly and ate fresh Mahi mahi (aka dorado) and coconut shrimp. Excellent food. Complementary after dinner liqueur.
Setting is a 100 year old coquina house with giant ancient bougainvillea shading the patio. The place is not well known, I think, and small so we didn't have a lot of loud company.
The Burguer House--Across from Sabora's on (I think) Av5 between Calle 3 & 5 Sur. The manager of this burger shack is the daytime waiter at Sabora's. He opens at 7pm. He has a list of about 20 hamburger variations, including a shrimp burger.
I am a burger aficionado and these are the best burgers I have ever had (take that, Five Guys). $6.50 US with to-die-for fries.
Ambiance? Well (if it shows up) the picture says it all. No drinks, so buy the at them OXXO down the block and bring them with you. The owner will not turn down a beer himself.
