We stayed at El Cozumeleno for two weeks in July. We found it a great hotel despite complaints in postings about the food that I read when researching our trip. Most AI's eateries are not gourmet restaurants but do allow you to not worry about where your next meal is coming from.
Scuba Du is the dive shop on the grounds. Ocean Tours does snorkeling tours and non-diving things. I did my first dive in the pool at El Coz and went with Scuba Du for the open water dive in the Discover Scuba course. I had buoyancy problems so I elected to use a private instructor and went three more times with her. I am now becoming certified--partly at home--and will return to Cozumel for my open water certification.
Scuba Du is also the dive shop at El Presidente, which is an expensive hotel; I'm not aware of an AI plan there. It is almost as far south as El Coz is north. The difference is that dive shops are located south of town unless they have a "branch" in a northern hotel. It will be easier to get to a shop if you stay south of town unless you use the shop in a north hotel. El Coz is almost the farthest north you can go. It would cost $8 one way to town in a taxi from El Coz and more if you go farther south to a dive shop. You can also rent a car (NOT AT EL COZ $$$) from many places on the island.
There is a wonderful site for information about hotels online--travelnotes and cozumelmycozumel about the island. There are boards on these sites where divers rate their stays. Another great resource is the Can-Do Cozumel map that shows reef and dive sites as well as hotels and other places. It costs a couple of dollars and can be ordered online.
You may also want to do research online about dive shops. You can stay at one hotel and use a dive shop from another if you wish. The two don't need to go together unless convenience alone is a huge issue. Sometimes dive shops have you go to their location, sometimes you meet them at the main pier right downtownl. Most of the businesses, including dive shops, will correspond with you via email about what they offer and you can easily make plans ahead of time.
Since I have not stayed at the southern hotels, I can't give you personal recommendations, but I do know the island. This is a list from my map of some hotels in the south zone from closest to town to "way down south"--Barracuda is closest t to town, then Plaza Las Glorias, Park Royal and La Ceiba; Presidente is south of the International Pier where the largest cruise ships come in, then Club del Sol, Fiesta American, Reef Club, Occidental Allegro, Iberostar, Occidental Grand. (Hotels are always changing names so...) Iberostar is an AI and I read happy divers reports about the stay there. While it is very far south, Palancar reef is just offshore which provides lots of diving depending on your level of expertise. Most shallower dives seem to be a bit closer to town.
All that said, if you want your S.O. to love diving, the dive shop you use is really important. See if you can find recommendations and make that decision. Find out where they are located and go from there. The island is small so traveling the entire length of the west coast north to south doesn't take forever.
Cozumel is a wonderful island. Eat at Casa Denis if you can and try the sopa de lima (lime soup). If you have more questions, feel free to be in touch.