Cağaloğlu is the slope between Sirkeci and Sultanahmet — small, easy to walk through unnoticed, and the home of Istanbul's two most overlooked institutions: the 1741 hamam that's the most famous in the city, and the Sublime Porte gate that ran six hundred years of Ottoman foreign relations.
Two and a half kilometres, gently uphill, with a hamam at the top if you want to stop being a walker for an hour. Start at Sirkeci Marmaray; cross south into Cağaloğlu. The Bab-ı Ali gate is the first landmark — the surviving doorway of the Ottoman government complex, where foreign ambassadors dealt with the Sublime State. The name literally means the high gate.
Climb Cağaloğlu Yokuşu through the streets where Hürriyet, Cumhuriyet and Milliyet had their newsrooms across the twentieth century. Most have moved out; some buildings still stand. Cağaloğlu Hamamı is at the top — Mahmud I, 1741, working baroque-Ottoman bathhouse with separate male and female sections. Sultanahmet T1 is two minutes further on, the dome of Hagia Sophia rising on your left.

