Suites Bahia is in town and across the street from the pier where Aldora, Blue XTsea, Deep Blue and other ops pick up.
Rooms are in the USD 40 a night range I think. Aqua Safari couple blocks south is in the same price range. I've stayed at the Vista del Mar last winter for USD 50, beautiful room with private balcony overlooking the waterfront (low season rate, prices go up around December 15).
You might be able to book these and save money on Flight+Hotel using the Orbitz Entertain coupon.
http://www.scubaboard.com/forums/cozumel/312371-orbitz-200-vacation-discount-code-changes-2010-200entertain.html
If not using a coupon, cheaper options include Hotel Pepita on 15 Avenida, US 32 a night, 2 queen beds, fridge and A/C in the room, nice courtyard, free coffee and drinking water, reasonably clean and a 5-10 minute walk to the pier. Booking by phone only.
Hotel Pepita Cozumel/Adventure Tours Mexico/Accommodation/Hotels Cozumel Mexico/Hotel Accommodation Cozumel
If really on a tight budget, you can dorm at the Hostelito for USD 12.
Hostelito, Cozumel, Mexico: Book Now!
None of the above except Aqua Safari has an in-house dive shop, but there are so many ops on Cozumel that it's easy to book the diving separately.
Barracuda is located further South but still within a reasonable walking distance to town. Staying at Villablanca will require that you rent a bicycle/motored vehicle or take taxis.
Cheap ways to eat include buying empañadas from locals in the morning (look for signs on Avenida 5 between Calle 5 and Calle 9), bread and pastries in the bakeries (recommand Zermatt on Avenida 5 near Calle 2 or 4), having lunch at Molina's (tacos, huaraches… they're located inside the Mercado Municipal behind all the produce stands and close at 1 pm)… I could go on and on, but there are plenty of places to eat cheap good local food, especially at lunchtime, if you stay away from the waterfront and Plaza areas.
In the evening, well worth spending more to try Kinta (Ave 15 near calle 2), awesome fusion cuisine, and many other great restaurants. My other favorite so far is Los Otates for the perfect tacos al pastor.
Look at Christi's Restaurant list thread.
http://www.scubaboard.com/forums/cozumel/124024-christis-restaurant-list-updated-but-not-exhaustive-4.html