If you’re looking for a cheap and comfortable hostel perfectly located behind the mosques in the old city than you should just book Antique hostel and stop waste your time.
Antique Hostel is 4-5min from the Sultanahmet tram stop and has some of the shared rooms in the basement (where I stayed too) but nevertheless it was still cool as it had clean 6bed rooms, a floor with lockers and separate toilets and showers. I liked to start and end the day on the terrace with the Bosporus view and mosques in the neck- this city has so great vibes!
Berke (the receptionist) was very nice and always available for a talk and with his smile makes everyone feel welcome. Thanks for the good time and next time I’ll stay longer and try to get us milkshakes :)