element:Accross from the Plaza La Glorias is what has been refered to as the Cozumel Walmart. You can get anything basic you forget or that is to heavy to carry and at good prices.
Last year i bought shaving cream, razor and some 3.99 red wine that I liked enough to bring a few bottles home and enjoy. Supper cheap to. Much cheaper than at my hotel.
I know visitors to the island often think that Chedraui is the coolest thing since sliced bread. However, it is very inconsistent, so don't always count on it to buy things you've forgotten. You'd be surprised at some of the things you would expct to find there that they do not have or the things they run out of for weeks at a time.
Also, some of the basic things you mention may cost you significantly more at Chedraui or on the island in general. For example:
shaving cream...$7 a can
hair dryers...$25 to $40 for a very basic one (Chedraui doesn't even sell them, you have to go to a specialty store)
4-pack of AA...$5 to $6
Chedraui is getting better, but FAR from Walmart and I still miss American grocery stores for the consistency, selection and cleanliness more than anything else.
Anyway, have a great vacation!