To find all three of your criteria may be difficult.
If you require all three of your criteria, and budget is not important, you may want to check out Cozumel Palace $$$$. Nice pool, decent AI Food reports and a nice enough beach area. Otherwise, you may want to consider eliminating the AI requirement to open up more options for your hotel/pool/beach enjoyment. Cozumel AI Food reports are ...well.. hit or miss. Most AI Food reports you find for Coz are poor to medicore to OK.... Overall, Cozumel offers so many wonderful restaurants in town, that it really would be a shame to miss this part of a visit.