Can your hotel be reached directly by traim or train from the airport(s)?
Having recently stayed here and traveled from/to both airports, I can tell you that the Ataturk airport is super easy by metro. The International airport (Havalimani) is a little more tricky in that you have a range of options. We went via coach and ferry then metro. Hope that helps
Get an answer from Sultanahmet Cesme Hotel staff and past guests.