Should I use a bank ATM at the airport or wait until we get to our hotel near the Blue Mosque. Are there banks in this neighborhood?
There is an HSBC Bank (based in London) fairly near the Blue Mosque with an ATM that should be reliable. You can also ask at your hotel, but HSBC has a good reputation and should be fine to use the ATM.
Thank you. I know there are lots of choices but I wanted to use a reliable bank and machine.
They are all reliable in Turkey but comission rates are quite high when withdrawing cash. It is 15-20 % .
Bank of America has a special aggrement with TEB bank (Turkish Economy Bank) . No commission at that bank.
I'll just add if you map your hotel on Google, usually several filter buttons show up across the top, one is usually "ATM". If it doesn't appear for some reason, you can just type ATM in the search area and it will show you the closest to the hotel. As I recall there was a big bank of ATMs between the Blue Mosque and Aya Sofia, depending on your research you can pick the one with the lowest fee for you and will have more than one option if one doesn't work for some reason (google coordinates: https://maps.app.goo.gl/83TYPyW3ZqhXvqqM7)
As CL mentions, there is a set of ATMs (look for bankomat in Turkish) on Divanyolu Caddesi, adjacent to the Aya Sofya, just near the tram line. But there are lots of ATMs around Sultanahmet, and all the Turkish bank ATMs seem reliable.