Topkapi museum holds the most ostentatious, almost embarrassing, collection of riches you're ever likely to see. Including Memet the fourth's emerald handled dagger; which Peter Ustinov failed to get his hands on in a bungled burglary attempt in the 1960's Oscar winning film Topkapi. Although why he ignored the Spoonmaker's diamond(more of a boulder than a rock) still remains a mystery.
Undoubtedly the most informative site you'll find on Topkapi; this is the labor of love of an electronics engineering professor; and what it lacks in aesthetic refinement it more than compensates for in rich content. This site gives all the historical background on the exhibits; then embellishes it with folk tales and anecdote(why is it called the Spoonmaker's diamond?).
After the Treasury the male daydreamer usually heads for the Harem; with rooms for up to 600 concubines. It does get busy and you have to buy a separate ticket, so it's best to do this when you first arrive, and plan the rest of your visit around it.
Tucked away in a distant corner is the Chamber of Holy Relics. It's an atmospheric place, where women will have to cover up, but it's worth it to see; Moses' Red Sea staff, Mohamed's hair/ footprints and part of the skull of John the Baptist among other artifacts. From the site it's clear that there is a lot to see, and once you have been bitten it will be hard not to go back.