Nobel Hostel is a nice hostel, localized right at the Sultanahmet Square (where you have the Blue Mosque, Hagia Sofia etc). No lockers, but we felt really safe. The staff was unbelievably kind, helping us to book day trips, boat tours, turkish baths, belly dancing and everything. I would definitely recommend it!
Tucano House was a great option! Very well localized, nice people around, good food on dinner, cool daytrips, everything perfect! I definitely recommend it.
Citystay Mitte is a great hostel very well localized (next to TV Tower). Staff was nice on telling me where I could find the things I was looking for. It would be better if they had a kitchen, but that's ok. The let me use the microwave. I've already recommended Citystay :)
Barnacles is a WONDERFUL hostel, one of the best I've been! The staff was really kind and helpful and the location was perfect. The kitchen is very useful and a nice place to hang around and meet people. I've stayed ther last Christmas, and they gave us free dinner, gifts and we also had a Santa Clauss there. They made my Christmas unforgettable.