Topkapı Palace was the administrative heart of the Ottoman Empire for nearly four centuries. It is not a single building but a sprawling complex of courts, pavilions, and gardens on the promontory above the Bosphorus — a city within a city that could house 4,000 people at its peak. The four main courtyards take you progressively deeper into the imperial world, from the outer public court (where the Imperial Mint still stands) to the innermost Harem.
Allow a full day, or at least a serious half-day. The Imperial Treasury is the most visited section, with the famous Topkapı Dagger and Spoonmaker's Diamond. The Harem section requires a separate ticket but is absolutely worth it — the tiled apartments, the golden cage where princes were confined, and the corridors connecting the Sultan's private world are unlike anything else. Book tickets online in advance in summer; the queues are long and the site closes early.