My wife and I stayed at the Eris for one week in April/May 2009.
I have stayed in worst hotels and I have stayed in better hotels.
I would say the restaurant is a hidden gem in this hotel. A great view of the Bosphorus, good food (especially the breakfast), and a server that took pride in his profession and went out of his way to serve you.
They have paid internet onsite but you're better off going to one of the numerous internet cafes in the area as it was unreliable and slow.
I rated the cleanliness poor because the entire hotel should have a thorough cleaning. The most important thing though was that the beds were comfortable and clean. The rooms are quite small (probably the smallest room I have stayed in) but I don't expect you will be spending much time in it other than when you're sleeping. The bathroom was very clean with lots of hot water and good pressure.
Although it is out of the way behind the Sirkeci train station, you're within walking distance to the major sites in Sultanahmet and a tram stop is just around the corner.
I do not know if there are boxes behind the front desk but there are no safes in the rooms.
If you're looking for a budget (emphasis on the budget) hotel with comfortable and clean beds I would recommend the Eris.More