Çengelköy is what Istanbulites do on Sundays — except on weekdays it's quieter, the breakfasts longer, the same ferries running. The walk is built around the meal: kahvaltı at Çınaraltı for an hour or two, then the sahil south to Beylerbeyi Palace.
Three and a half kilometres, gently downhill mostly. Arrive by ferry from Eminönü or Beşiktaş; the pier is a hundred metres from the square. Çınaraltı is the heart of the village — a centuries-old plane tree, restaurants under it that have been serving the full Turkish breakfast for generations. Order menemen and twenty small dishes: cheeses, olives, fresh bread, honey, jams, sucuklu yumurta, and the small Çengelköy cucumbers the village has grown since long before the suburbs reached it. Çay all morning.
Then south along the sahil. The Bosphorus is on your left, the wooden yalıs on your right, the 15 Temmuz Şehitler Köprüsü arching overhead about a kilometre in. Twenty minutes brings you to Beylerbeyi.
End at Beylerbeyi Sarayı — the 1865 summer palace, the one Sultan Abdülaziz built for entertaining European monarchs and the one Empress Eugénie famously preferred to Dolmabahçe. The outer grounds are free; the interior is paid and worth it. Beylerbeyi bus stop is at the gate.