One to consider is a Blackbeards liveaboard. It's $959 all inclusive except for $100 in fees/fuel surcharge - plus crew tip. It's like camping at sea and you'll be sharing an area with several others - it's all bunks. But they do a lot of diving for the money - up to 19.
So all you'd have is the cost of the flight to Nassau and cab to the boat.
Bahamas Scuba Diving Liveaboards - Blackbeard's Cruises
Cozumel can be very reasonable also. Flights should be more affordable than Roatan or Bonaire. I think you save more money by doing the bag drag from Cancun also - it requires taking a bus to the ferry and back. Some friends stayed at Villa Blanca Garden Hotel for under $700 including a single room, 15 boat dives and 3 meals were like $20 more/day. There's also a so/so shallow shore dive there in some rubble. They work with 5 dive operators nearby.
Diving in Cozumel - Villablanca Garden Beach Hotel, Cozumel I don't know Cozumel but I don't think it's near much. My buddy walked to town once - about 2 miles. They also offer 4 night packages - but that's only 3days diving.
Roatan's West End can be dirt cheap also. Places like Posada Arco Iris are $40-48ish per night for a studio with full kitchen. A one bedroom is $10 more. There's several small markets in the area for staples - one even sells some produce and meat. Food can be anything from street vendors grilling meet just outside your door to Sundowners Bar on the beach for sandwiches up to one of the finest Indonesian restaurants in the Caribbean. We never paid more than $5 for lunch or $25 for a steak dinner - at Argentinean Grille which fronts Posada. All the nightlife on Roatan is in that area also - the pub crawl later in the week is a good time.
Posada Arco Iris - Lodgings
Coconut Tree Cabins nearby has studios starting at $45/nt. If available, some with full kitchens. I think it's the same price. Lots of general West End info here also:
Roatán, West End | Scuba Diving | Roatan, Bay Islands, Honduras | PADI - we dove with CTD and I recommend them. Depending on your standards, you can find rooms for $10-20 nt. at many other places also. More inexpensively, Chillies is a hostel there. They're owned by the same people who own Native Sons, the other dive operator I recommend.
Chillies: Best Budget Hotel on Roatan Island
Diving is 10/$300 from any number of operators - there must be a dozen within a 1 mile stretch. Night Dives are $40 more. There's one shore dive there but access is more difficult - so is finding tanks to rent as most ops are boat based. You don't need/want a car (liability issues) and a cab from the airport is $25 one way. The only other expense is $40 to leave.
One last thing if you're flexible on timing is to wait until Low Season starts. Typically that's April 15th or May 1st in the Caribbean. You'll save quite a bit. We plan our trips for late April/Early May - it's not summer so kids are still in school so less people travel then.
Grand Cayman and Turks & Caicos are the 2
highest priced places I've dove. You won't find accommodations on Grand Cayman (as a single) for under $90 night, food is exorbitantly priced - even in markets - but there's a Burger King, several Subways, Dominos etc. Hardrock Cafe and Margarataville downtown also. Boat dives are about 2/$100+ from every operator. You can shore dive reasonably at a dozen sites but that requires $2-300 more for a car with CDW. Most sites have an onsite operator for tanks - they own to the waterline and do not allow other rentals on-site. Cayman is much better with a group so you can quad share a 2BR condo on the beach reasonably - they start at $250/nt. and up.