Grand Cayman is about the most expensive dive location in the Caribbean. The CI$ is fixed at .80 to the US$ so you're 20% down going in. If we take your budget of $2200 and subtract $900 for flights that just isn't realistically possible. The cheapest hotel is around $100/nt and meals average $40-50 for decent options. All the cheap fast food U.S. chains are there but they're also higher. Boat diving is typically 2 dives/$100 and your b/f's O/W course will cost you around $500. The only plus is that all the dive operators pick up for free anywhere along Seven Mile Beach. With a car (another $400ish) you can shore dive at about a dozen sites but only 3 are really good. Plus would you be comfortable without a guide? - they're extra also.
I don't see how you can possibly do it. We did Cayman cheap once and it cost us almost $2000pp. We cooked most of our meals - groceries are real high also. It's literally the only dive trip I've ever been on where I had to hit the ATM to have enough cash to get home.
Cozumel is mostly drift diving if that's a consideration. You can also fly into Cancun and do the "bag drag" to Cozumel - bus/taxi to the ferry. It's still cheaper than flying directly to Coz - how much depends on flight deals then. Villablanca Garden Hotel is an affordable option - they bundle packages with 3 or 4 nearby dive operators. 2 miles to town from there though and cabs aren't especially cheap either - the ride from the airport is farther.
Honestly I can't think of anywhere else except Florida that's possible on your budget.
Roatan is cheap if you stay locally in the West End but the flights in May/June will be $700pp. Even then you're looking at around $350 for lodging (1 br. apt) dives at 10/$300pp. - your b/f's cert is around $325 and food is cheap to affordable. Costs you $50 to get to/from the West End and $80 to get off the island. You wouldn't need/want a car but you do the math...
Check Belize also but I think it will be more expensive to get there. Plus you have to get to Ambergris or somewhere in South Belize to dive - that's usually a $150-200r/t local flight. Also the better diving there often costs more since the ride out to the Barrier Reef can be an hour. Some of those dives are upwards of $150/200 for 2 dives.
Check flying into FLL or MIA then over to the Bahamas also. Sometimes that's cheaper if you fly Southwest, Spirit or Jet Blue down then Bahamasair over. There's also a ferry from FLL to Grand Bahama (Freeport) but it's not much cheaper than flying. The issue there is it's all boat diving - on Nassau there's two operators, on Freeport about 5. 2 tanks on Nassau are upwards of $100 also and food/lodging prices are almost as bad as Cayman. There are a few older, slightly dumpier hotel options - Expedia lists them. One of the B&B's on Nassau does a package deal with Stuart Cove's also.
After Palau, everything in the Caribbean is going to be a disappointment...
