Es gibt eine Metro, die direkt vom Flughafen - im Gebäude zwei Rolltreppen nach unten gehen, immer den Schildern nach - in die City fährt. Der Preis liegt bei 2 Euro. Warum nimmst du nicht die? Ich mach es immer so.
Unter folgendem Link findest du diese nützliche Info:
http://www.turkeytravelplanner.com/go/Istanbul/Transport/airport_sultanahmet.html
You can travel from Istanbul's Atatürk Airport to Sultanahmet, the center of historic Istanbul (and the best hotel area) completely by Metro & tram in about one hour for TL4.
You arrive in the International Arrivals terminal, purchase your visa, pass through Immigration (passport) and Customs control. Exit the secure Customs area, turn right and walk to the end of the terminal watching for signs to the Hafif Metro ("Light Rail System").
Stop along the way to get some Turkish Liras from currency exchange offices or cash machines (ATMs) in the Arrivals hall. No matter how you plan to travel into the city, you will need some local currency.
A guy will come up to you as you walk and try to get you to take a shuttle van into the city. (It happens to me every time.) I tell him Istemez! (eess-teh-MEHZ, "It's not wanted"). The problem with a shuttle van is that it circulates through the city going to lots of hotels. If yours is the last one, you ride around a lot. There are other dangers as well. More...
Go down the escalator, through the sliding glass doors, turn right and follow the Hafif Metro/Light rail system signs along the broad underground concourse to the Havalimanı (Airport) Metro station on the left at the end. This concourse beneath the parking garage connects the Domestic and International terminals.
Buy one or two Metro tokens (jeton) at the booth—the price is marked on a paper sign in the window, and should be TL2 each. You'll need two tokens to travel from Atatürk Airport to Sultanahmet, Eminönü or Kabataş, three to reach Taksim Square.
Click here to download a map of the system (363Kb .pdf).