Where can I buy and top up an Istanbulkart at Istanbul Airport for travel to Sultanahmet?

At the airport, you can get an Istanbulkart from a staffed counter rather than a vending machine: go down to level -2, where the service booths are located. The staff can top up the card with your chosen amount at the same time.

You can exchange cash before buying the card at a currency exchange between exits 9 and 10. If that particular counter is closed, there is another exchange office nearby.

After topping up the card at the level -2 counters, ask staff which platform to use for travel toward Sultanahmet. A Havaist desk is also reported near the exchange area.