All I can tell you is that you DO NOT want to make out of country your first dive unless its a very shallow dive in 20 ft of water. I belong to a dive shop and there are too many sad stories of divers getting certified.. flying out to Cancun and experiencing 20 minute dives and watching bubbles while rest of the boat is down under for an hour. Think of it in terms of finances. A 1 week stay with 5 days of diving in lets say a Cozumel, Mexico costs 1400 not counting food. Each dive comes out to about $50 per dive pending you have your own gear.. if not then you are paying $100-$200 extra in dive gear per dive day. Naturally you would seek to maximize bottom time and thus get the most out of money that you are spending. Trust me.. it is really really boring bobbing up and down on a boat watching bubbles in 120 degree weather.
So... make first 10 dives locally.. maximize your bottom time.. get to a point where you are comfortable under water, know your gear and can get 45-50 minutes to a tank and then go off to experience out of country adventures.
While I generally
agree with the above advice, especially the last paragraph, I would note a few differences. First, the OP appears to be making the trip not to dive but for other purposes so the dives are simply an add-on. That makes the way one thinks of pricing a bit different. He is already doing the hotel whether he dives or not, etc. already...
Second, the Yucatan can get really hot some times of the year. I think the all time record high for Cancun is about 104. It can get much warmer inland (I have been in Merida at 110), you won't ever find 120 degree weather in Cancun, Isla Mujeres or Cozumel.
Finally, I while agree dive trips are spendy, I am lost with your pricing. Dive vacations are spendy and there is no way around that. But there are a great many price points and folks have tons of choices and some tricks.
If I reverse engineer your math, ($1,400 divided by $50/dive), I get 28 dives in 5 days. Was that for one person or two? The same with gear rental. If I use Dive Paradis as reference in Cozumel, you can rent the basics for $15 per day. Add a short for another $7. If you like, a computer for another $10. That is way less than $100 to $200 per day. I don't know anywhere that charges more than $100/day for basic equipment.
Two samples to Cozumel (excluding air, 7 nights, no food, 5 days diving -- 15 tanks total), using Dive Paradise (not the best operator on Cozumel but they were both large and decent last time I went): Single going to Fiesta Americana in the High Season -- $1385 plus any rentals 0r $92 per dive
Or, same parameters except two divers split the cost of $1100 ($550 each or $37 a dive) at Coral Reef Inn plus any rentals.