If I only had 1 day I would want to be on the beach as much as possible.
Breakfast, El Pirata ( if they still serve chiquilas).
Lunch, Playa Maya, Coconut Shrimp,
& shrimp ceviche
Dinner, La Tarraya.
After dinner, work your way north up the beach hitting as many beach bars/clubs as you can.
no shoes, no problem at any of these.