A lot depends on how much time & money you have as well as how comfortable/confident a diver your nephew will be at first.
For ease and economy you can't beat the Keys. Capt. Slate in Key Largo does a Friday morning "creature feature" where he feeds barracuda and eels (sometimes some nurse sharks show up too) and you get to fondle the critters (I'm actually not a big fan of acclimating fish to humans but your nephew will have a blast bragging to his friends about his encounter!) Most dive sites are in the 30-40ft. range so he can't get into too much trouble. You can work your way down the Keys and even take in the human circus in Mallory Square at sunset and Margaritaville in Key West (Key West has the worst diving of the Keys but the most topside activities). If you go here, I'd also suggest a night dive. Tavernier Dive Center does a nice job with these and, again, hard to get into too much trouble. I agree with the others that weather and conditons can vary so be sure to bring seasick pills (just in case) if either of you are prone to turning "green".
For great diving, both Cayman Brac and Grand Turk have exceptional diving but might require a higher degree of skill than he'll have, at first. Neither one has much of anything to do topside. (Also, Grand Turk water temp is a little colder that time of year.)
Have you considered someplace like Cozumel? It's fairly cheap, the diving is good and there's stuff to do topside (tours to the ruins, etc. etc.) My first ocean dive was in Cozumel and once I got over the surprise of suddenly finding myself 80 ft. down with crystal clear viz I really enjoyed the drift diving.
Again, lots of choices but just thought I'd throw in my 2 cents. Have fun!!