We will be in Istanbul for 3+ days in April. How prevalent are ATM's at both the airport and in the historic district? I presume the currency dispensed is Turkish lira, right?
First, I always avoid airport ATMs so cannot comment on airport ATMs. Second ATMs are prevalent nearly everywhere since the primary users are the locals and not tourists. You should not have any problems find them. In country ATMs only dispense local currency.
Istanbul Ataturk Airport has a "chorus line" of 4 or 5 ATM's, each from a different major Turkish bank, that you will pass on your way out of the airport. They are the same banks that you will see all over town. Istanbul, being a large city, has ATM's all over the place, and as Frank said, they are primarily for residents; you won't need any help finding them. Yes, they dispense Turkish lira.
One "warning" about money, though. If there's a place to change money back at the airport upon departure, I never found it. So, either allow extra time to convert your remaining lira back to dollars, or spend down carefully and use credit cards toward the end of your trip to avoid having excess cash.
I had no trouble finding ATM's in Istanbul. I don't remember if I took cash at the airport on arrival or not - my hotel provided transport.
In the last few months, I flew through Istanbul on 2 separate trips, so 4 times in the airport. I am pretty sure there are no ATM's before go through passport control.