I have been diving Cozumel for over 30 years and have noted that for most dive companies in the last 15 years will stay within a 15-20 minute boat ride of where they pick you up. For example, if staying on the south end of the island (Allegro/Occidental), you will dive Palancar Gardens, Delila, Cedral, Francesa, and Santa Rosa (now closed) over and over. All outstanding reefs and you won't be disappointed; however, if you are staying for a week or more and diving four dives a day, you will want some more variety. My favorite way to dive there is with my group of three other guys with whom I have been diving for decades, stay in town, and hire a private dive company that keeps the number of divers to four or less per dive master and no more than two dive masters (max eight divers). By being in town, it makes the economics for the dive company favorable to dive both the north end and south end given that the current runs south to north so if diving Punta Sur you will drift north allowing you to pick any of the reefs south of Santa Rosa. Likewise if you want to dive north you can start with Santa Rosa or north of that and drift toward town. Time and gasoline are factors that the dive company have to consider. Large slow boats equal limited area of dive sites; fast and small boats increase your range considerably and allow the dive company to be more flexible.
I recommend looking into Blue Mystic divers. Nico is the owner, has been living in Cozumel for six years, keeps the groups small, uses fast boats, is very experienced, and provides a seamless experience. Additionally, we dive the reefs we want with him. There are exceptions, for example, Chun Chacaab and Maracaibo are always "iffy" due to the capricious currents which can limit safe access for the boat as well as the need to be an experienced diver in general.