Address Topkai Palace, Istanbul Map, Website
The chance to see a real palace, especially one as ornately decorated and treasure filled as Topkai palace should be a draw for most kids. The grounds are huge, though, and the food options inside are passable, but not great. Consider bringing a picnic lunch, snacks, and an inflatable ball so that you can take breaks from the collection as needed.
My kids seemed fascinated by stories of palace life, and details like the fact that the harem pool used to be filled with milk. It is well worth reading up on palace history before you visit so that you can help bring the buildings alive for your children.