From the Airport
Istanbul has two international airports. Atatürk International Airport is located on the European side, about 24km west of the city center. The smaller Sabiha Gökçen International Airport is located on the Asian side, about 35km southwest of the city center.
Atatürk International is the city's main airport. Taxis are the most convenient option, and cost about 35TL to Taksim and 30TL to Sultanahmet. Express buses, known as the Havaş, depart every half-hour from 04:00 to midnight to three of Istanbul's main bus stations (Taksim, Etiler, and Kozyatagi). These will set you back 10TL. A public bus line runs from the airport to Aksaray, near Sultanahmet and costs around 2.50TL. Travel times vary depending on traffic.
The M1 metro terminates at the airport, at the Havalimani-Ataturk station. One token costs 1.50TL. The other end of the M1 is Aksaray station, near Sultanahmet. With a transfer or two to another rail or tram line, it is possible to get just about anywhere in Istanbul. Of course, it may be inconvenient if you're carrying lots of bags.
The Sabiha Gökçen services mostly budget airlines. A Havaş express bus departs for Taksim and Kozyatagi. It costs around 15TL. As at Ataturk, they run from 04:00 until midnight. A taxi to the European side can cost upwards of 60TL. Private shuttles are available which can cut the cost in half.