We will be staying at the Royal Caribbean and would like our groceries delivered as I am not sure there is a grocery store in the area besides the small one at the hotel. Any ideas?

Assuming you are in The Royal Caribbean (Islander, Mayan...) group in Cancun, Hotel Zone.

You could easily take the Centro bus to major grocery store Chedraui and save a ton of cash.

Or

Use the service some of our friends use to stock up before arriving, loQsea.