A good suggestion re: hamam.

Realistically, you won't see any "afternoon". By the time you clear passport control and baggage, then get into the centre of town, it's going to be into the early evening.

If the hamam is too much for you, I suggest a relaxing meal in one of the rooftop restaurants; several hotels have very good options (Swissotel, for example). There are outdoor or indoor options, depending on the weather and when you arrive. "5 Kat" in Cihangir has a great atmosphere and wow-factor views - they have a website or your hotel concierge could book ahead.