There won't be rustic beach side bargains. The few beach side accommodations are on the south end of the island in luxury resorts. In town there are hostels at bargain prices, several nice hotels in the downtown area that are bargains, and lots of medium price rooms at many of the hotels.
Much of the shore line of the Western side of the island, is inside the Underwater park, and you must be accompanied by a Marine Park Guide. . . There are some diving spots, from the southern (mid island) area and going north. Much of this area will be shallow and sandy, with boat traffic over head. Not suitable for most divers. Night dives in this area are very popular, and several dive shops can rent tanks. . . Some hotels in this area have dive operations as part of the package, Good places to stay if they're not booked well in advance.
I hope this doesn't sound negative, it isn't. World class diving in the park from boats, Good visibility, but scattered coral heads available from shore. Dive guides for every 8 divers. Careful attention by guides for beginning divers. And freedom for experienced divers. . . Something for any diver.
Read the "Cozumel" forum. . . and make reservations early, this is a very busy season.