Despite being a big fan of Cozumel and of course, opinions are subjective, I can’t think of anywhere that would fulfill all those criteria, IMO.
I can make some suggestions for you to research and perhaps others have better ideas.
Intercontinental and Cozumel Palace are considered higher-end/pricy hotels. They have /had day passes but are not somewhere I would consider on a cruise ship day (maybe land vacation since they are not the type of accommodation we stay in, as we stay extended.) So no personal experience with either or food, but not what I consider beautiful setting. YMMV.
Buccanos beach club has day beds and better food.
Nachi Cocom popular quieter beach club with mixed reviews recently.
Chankanaab has private area Cabana Beach.
Mr Sanchos (busy beach club) has private VIP villas for overnight, not sure if you can have them for the day.
Hotel B boutique hotel.
As I said, it depends on your expectations, and what you consider most important, but I know you will not find what is available on other islands or Caribbean destinations. We have spent many wonderful days on cozumel but luxurious is not a description I would use.