It sounds like you might have already left Istanbul, but I will try to answer it anyway. It all depends on how long time you have got and what your kid's interests are. Most of the main highlights that any visitors must visit are in Sultanahmet area, including Hagia Sophia, Hippodrome, Blue Mosque and Topkapi Palace.
You can make the Hippodrome interesting if you do some reading and tell some stories Nika Riot and chariot and gladiator fights. The armory and treasury sections of the Topkapi Palace should be very interesting for your sun. At the palace, go all the way to the last courtyard and have the view of the Bosphorus and the Maiden’s Tower (Google it for interesting legends about the tower)
The Underground Cisterns in Sulatnahmet area is a perfect place to visit with a 13 year old. The ambiance and acoustic are just amazing (Tell him the mythological story of the upside down Medusa head)
Kids love the Bosphorus boat tour. You can visit Rumeli Castle on the European side or the Genoese Castle at the end of the Bophorus line.
There are three other kidddy attractions for the kids and they are all located around the Golden Horn area:
1-Miniaturk (a miniature park),
2-Rahmi Koc Museum (a private industrial museum which your son might find interesting for its old racing cars, sultan’s carriages, locomotives, passenger ferryboat, amphibious car, and model toys and some activities for kids, including cutaway car, aero plane, scientific experiments and cutaway domestic goods)