Most divers prefer to go straight to Cozumel and set up base-camp there. Others prefer to stay on the mainland and travel up the coast diving here and there. You can stay in Cancun and dive at Cozumel if you wish.
There are dive centers all along the coast and you can stay anywhere and find tanks and a boat to take you out. Many of the dive centers employ Europeans and Americans, so English is spoken quite often.
From Cancun to Tulum there are numerous resorts, cabanas at the beach and small hotels. Many resorts have dive centers and most if not all beaches have a local dive center and boat. After Tulum there is not much except Punta Allen until you get to Majahual where you will find the Chinchorro Reefs. Beyond Majahual is Xcalak then you are in Belize.
In Majahual there is a reputable dive center at Maya Ha resort which is a nice place to stay and close to Majahual town.
TIP:When you dive be sure to check with your dive operator to know if they are affiliated with a Chamber Service. Typically each diver pays $1 dollar per day to have full coverage against diving accidents. A form is completed and you sign it. Do not assume you are covered. BE SURE!