Recommending exact dive sites might not be fair to you, as your skills may or may not allow you to dive them.
ALL our dives are drift dives on Cozumel. The Marine Park runs South to North along the island, between the island and the Yucatan, so there is a constant flow of current passing, through the channel allowing us to drift dive. This brings massive amounts of nutrients from the Caribbean Sea to the reef and is why our reefs are so healthy and abundant with life.
Certain times of the year, the currents are tricky and can change directions (sometimes several times during a dive & even flow up and down the reef!), but in general, the current flows South to North and isn't super strong.
Some people get the impression that drift diving is a "fast" process, when USUALLY, the current is at a very slow & mild pace, and it is more of a gentile ride, slowly drifting along the reef at a pace where it is easy to see the reef life. Although there are occasions when the current is strong and it IS more like flying ... which can be fun in it's own right!
a reputable dive operator will take you out the first day or 2 to "easy" dive sites and evaluate your dive efficiency and then take you to dive sites that are appropriate for your level of expertise.
this will not take away anything from your dive experience on Cozumel. All the dive sites are amazing in their own right, shallow or deep, wall or "gardens" & mid-shelf reefs.
Be sure to let your dive op know when you make your reservation that you are a novice AND again when you arrive and check-in with them, just to make sure they know where you are coming from.
If at any point you feel uncomfortable with a dive selection, or profile the DM is giving, don't hesitate to speak up. Making a change so every one can have a good dive should be no problem for a good dive op & dive master. Ultimately your safety is your responsibility as a diver, so don't feel shy about speaking up on the boat or at the dive shop.
Tips on finding a dive op on Cozumel ... A Shark Tank radio show segment made form an independent poll taken here on the ScubaBoard & interviewing people I know who dive on the island.
Sharky's top dive op reco's ... a far from complete list of dive ops on the island, but the list runs the gambit of pricing and services.
...welcome to the family!