To go to Sultanahmet, passengers can either go to Taksim or Kadıköy and change vehicle for Sultanahmet area.
There are shuttles working between Taksim and Sabiha Gokcen Airport every half an hour. The name of the bus company is HAVABUS. The duration of the trip is about an hour and a half depending on the city traffic, the shuttle fee is 15 TL from Taksim you may go to Sultanahmet either by taxi or public bus.
Another route is to go to Kadıköy and take the ferry to old Istanbul. You can either take the E10 IETT public bus or Havabus shuttle to Kadıkoy (10 TL). You will reach Kadıköy in max 1 hour and the ferry to Eminonu will take about 25 min. From Eminonu you can either walk or take the tram to Sultanahmet.
To ride the IETT public bus and ferry passengers have to obtain Istanbul Kart, which can be purchased from the IETT kiosks near the bus waiting area.
All public transport vehicles and taxis are located in front of the terminal building at arrivals level.