we got 2 airpot perhaps you will use Atatürk airpot and you will have no trouble
There are two international airports in Istanbul, located on different sides of the city.
Ataturk International Airport (IST) is located on the European side and is only half an hour driving distance away from Sultanahmet. (please note that this is a rough estimate, it takes half an hour without traffic jam.)
The other one is Sabiha Gokcen International Airport (SAW), it is located on the Asian side. It is a fairly new airport although many flights take off from there as well. From Taksim, it can take 1.5-2 hours to go to Sabiha Gokcen airport on most days.