The FL Keys come to mind for a quick certification oriented trip, but if you're looking at going very soon the water may not be as warm as he'd like, or even the air if you're unlucky. Same with the Bahamas.
For a short trip obviously closer is helpful and non-stop better. I think places like Bonaire, Curacao, Roatan, Belize are great for checkouts but getting to these and really so many of the better Caribbean dive destinations from Boston requires connections that can make for a long travel day. I'd focus on closer/mainstream places like Grand Cayman, maybe Provo, maybe even St Croix. Start poking around at flights and see where you can get the best schedule. Flights also may also depend on when you go, since some flights may only be peak season or only certain days of the week. Since Saturday-Saturday travel is popular there's often more flights then but a 4 night trip doesn't allow you to do Saturday both ways either.
You might also look at Aruba again. While further, it's such a popular tourist destination with lots of flights you might still be able to work a relatively cheap/quick trip. Diving not as good with as many options, but likely to be way easier to get to than Bonaire or Curacao next door.