All of the rooms have kitchens or mini kitchenettes but there is no restaurant on-site. I don't like to cook either so usually what I do in Cozumel is go to Mega (large grocery store like a super Walmart) and stock up on fruits/snacks/cold cuts/beer.
Aldora boats typically stop at Mr Sanchos beach club or Playa Palancar for lunch during surface interval so you can buy food.
The Villa itself is approximately 20-25 "brisk" minute walk downtown where there are a plethora of restaurants. A taxi from/to centro should cost no more than 40-60 pesos (~3USD depending on exchange rate). I like walking so usually what I do is walk into town and take a taxi home. Villa also has bikes available for guests to use.
Food and restaurants is a hotly debated topic in Cozumel but let's just say there are plenty of options to satisfy every budget or lack thereof. In no particular order.. Most of these are a very quick taxi ride of a 30-35 minute walk.
(Please don't kill me if I missed your favorite restaurant..)
Los Otates
El Pique
Thirsty Cougar
Wet Wendys
Del Sur
Ohanas
Los Seras
Burrito Gordito
La Choza
El Moro
Le Chef
La Kinta
Casa Mission
EDIT: See Dave's reply above mine.