I'll throw in my $0.02.
I have dived Cancun, Nassau, and Turks and Caicos in the Caribbean. I would recommend Cancun or Cozumel since they are primarily drift diving conditions and I don't think great for beginners. Nassau was nice but only went diving one day.
The Beaches Resort in Turks and Caicos was where my then 13 year old daughter learned to dive. It's an all inclusive resort with food and beverage but can be a little pricey depending on the package. But diving is included with 2 tank morning dives and 1 tank afternoon dives. There is a 5 star PADI center on the resort and that's where my daughter learned to scuba (for an additional fee - which would have been the same price as training at home.). There are two other resorts in Jamaica as well.
best part about vacation is that the kids have a miniature water park in the resort. Dive in the morning. Spend time in the water slides in the afternoon. Have nice dinner in resort restaurant. It was absolutely one of the best dive trips with the family I've had. When in Maui and Kona I spent about $140 pp per day diving. Four day dives and two night dives for two divers and rental gear with tips really added up! And at the Beacphes resorts gear is also part of the package. I took all my gear last time but at least I didn't have to pay for my daughter's gear rentals either. And they do cater to beginner divers. Factoring what I pay out of pocket for diving the cost seems like a better deal all things considered.