Transportation from Ataturk to Sultanhamet for 4
 

Is public transportation easy? Are taxis reliable and hassle-free? Or is there another better option? We're leaving later today, arriving tomorrow morning.

Public transport is simple, but CROWDED. But your multi-day transit pass ("Istanbulkart") AT THE AIRPORT. You would get on the subway at the airport and transfer to the tram at Zeytinburnu. I would decide based on the amount of luggage you are carrying. You will likely have a seat for the subway portion since the line starts at the airport, but may (will probably) stand for the tram portion. You have to re-insert your card when you transfer.

May be too late but yes taxis are reliable. If you have arranged accommodation in the Old Town, most if not all hotels can arrange a very reliable transfer service to their door with prices as good or better than cabs.
I would not recommend the train, especially if you are jet lagged.

Thanks - ( we board in an hour )

Look at Efendi Travel. They offer airport transportation, reasonable. Hope you have a layover somewhere to book it. Have a great trip!

Happy, as it turns out, we did book Efendi Travel, on the web while laying over at JFK. It was inexpensive (about $35USD) and perfect (door-to-door). They were waiting for us with our name on a sign when we came into the arrivals hall.

Glad the airport transfer worked so well for you sf7307.