Eminonu is the main ferry hub on the old city side. From here you can reach Kadikoy, Uskudar, the Princes’ Islands and points up the Bosphorus, all on scheduled public services rather than tour boats.
Practical notes: pay with an Istanbulkart at the turnstile, the same card used on trams and buses. Kadikoy and Uskudar boats run roughly every twenty minutes from early morning until late evening. Island ferries are less frequent, so check the board before planning a day trip.
The pier is about ten minutes downhill from Hotel Yasmak Sultan. Coming back is a gentle climb, or you can take the tram one stop from Eminonu to Sirkeci.