I believe the Blue Hole is off of the island of Andros, the largest island in the Bahamas, which is just west of New Providence, the island on which Nassau is located. As SC and most of the operators are on the SW side of side of New Providence, they are on the part of the island closest to Andros and so some operators located there offer trips over to Andros. My understanding is that SC offers that trip as their out island seafari, an all day three tank charter that you have to book on island. I have heard the diving off of Andros is supposed to be outstanding, but we did not get the opportunity to make it while we were in Nassau.
The don't miss sites on New Providence include the "Tongue of the Ocean", a 5000 ft deep trench that runs between New Providence and Andros. It has the best coral and its pretty cool to look into the abyss. Also, try the Bond wrecks. These include several small props, sunken boats, planes and etc. as used in a number of James Bond movies. The Vulcan bomber from Thunderball is pretty cool, you can't even recognize it as it is just a frame covered with coral. Try doing this on a DPV and you can picture yourself right in the middle of the climactic battle in Thunderball. Pretty cool stuff.
Above all else, do the shark dives and be sure to get the video, as it will get plenty of play as you and your son relive the adventure. I just wish they had offered DVDs back when we did it as we have nearly worn out the tape.
There are on island coupons that SC puts in the tourist hand outs in the airport that can knock a few bucks off your tab. The bottom line is its pretty expensive to dive in Nassau, but you can get some unique adventure dives (sharks, DPVs) that nobody outside of the Bahamas offers (at least in this part of the world)