Flying Easyjet to Sabiha Gocken Airport requires a taxi transfer to Sultanhamet. Taxis are waiting outside the airport and the metered fare is around 70 Turkish Lira. There are only two issues. The taxis tend to be rather small and with four passengers and four bags it can be a bit of a squeeze. Journey time is about 45 minutes. The second issue is an almost complete lack of street signs in Istanbul. Have your destination address written out, and also a map or landmark to guide the driver.
Be aware that taxi drivers will try to over-charge tourists. Tell the driver where you want to go, and ask him how much it will cost. If he quotes you a fare, say no and look for another taxi. If he says "taximeter", that means he will charge you the correct amount, and the same price as locals. Taxis are fairly cheap, and should cost about 5ytl for a 15-20 minute walk.
Finding a taxi in Istanbul is simple (they seem to outnumber private cars). The main problem is avoiding them when you dont want one.
