Just a couple thoughts:
1) If you have kids or folks on the trip that are not at all adventurous, then consider AI for convenience.
2) If you have teens that normally eat you out of house and home, then go AI for economy.
3) If you have reasonably adventurous adults that are not whiny prima donnas, then go for eating around town.
Search this board for the ten million posts listing the best restaurants in Cozumel.
There are definitely some restaurants that can be a little pricey. We had steak and Lobster at La Mission, and it cost a bunch. I have eaten at Prima's a few times and it is not cheap. Good, but not cheap. (Note that both are central to the "tourist" part of town)
Personally I LOVE Guido's, so I don't mind spending a bit of money to have a real nice meal occasionally.
However, with a little bit of effort, or research or exploration you can find a lot of really good food for reasonable prices.
Trust me, the locals don't eat at Prima, La Mission or Guido's all the time. There are a lot of places that have good food at economical prices. Many are called "economicas". I found that if you get a little off the beaten path, you can find some great places to eat.
I found a little taco place just up the road from Prima's (away from the tourist area) The taco's were very tasty, and like 60 cents each. There is a little place called Comida Casera Tonita (or something very similar) where you can get a three course lunch for about $3.50 or so. Las Palmas was also very good and very reasonable. El Morrito has three places. The Tacos and Burritos at the Hotel Flamingo were outstanding.
Here are a couple thoughts to ponder: In your town, are there expensive and inexpensive restaurants? Of course. Some are way too pricey to eat at all the time unless you are Bill Gates. Are they worth eating at occasionallY? Sure. Are there some restaurants that offer good food for a reasonable price in your town? Sure. Which places advertise in the high dollar venues? The expensive places. Which restaurants are in the fancy center of your town, the economical ones or the high end ones? Isn't the "overhead" higher in the downtown areas and lower in the outlying areas? Who pays for the higher cost of floor space right where the action is? You, the customer.
Okay, so Cozumel is not all that different. In general the more economical places are a little away from the center of town, away from where the average tourist/cruise ship passenger will wander. In general the economical places will not be advertised on the cruise ships or at the hotels.
The people that live and work in Cozumel can't afford to eat at the fancy places every day any more than you or I can. We can justify more expensive meals because we are rich foreigners and because we are on vacation dang it!
I did a simple thing. I asked my dive guides where they eat. I asked some of the hotel staff what they recommend for just a normal meal. I also asked them for some good restaurants too, and they said Prima's and Guido's and La Mission etc. I asked the people that worked in the Dive Shop where they got their lunches, and that is how I found some places that were really good for low prices.
At Tonita and at Las Palmas, we see locals coming in with tupperware containers to buy food. At the taco place, I was the only Anglo in the place. All had really good food for LOW prices.
My recommendations are to skip the AI, explore the town, and find some great food choices. Have a couple meals at the popular places (expensive) that you found out about here on SB, but also ask around to find some great economicas. Support the mom & pop restaurants and save some money at the same time. Be willing to ask some questions, take some chances and walk a few blocks.
Just my opinions, and only because you asked.
Wristshot
Liquid Blue is another op that is recommended 
