I had a very lovely stay at Melisa's AirBnB. I definitely recommend staying in Beskitas over Beyoglu where most of the other options are available. You will find better restaurants, cafes, and it is easier to locate a taxi. I had no problem reaching one on the main street where the apartment is located, and it is a very quick trip to all the main attractions you will want to see. It was also very nice to be steps away from the ferry terminal if you would like to visit the Asian side, and just to sit and admire the view.
I found the apartment to have everything I needed for my short stay, though there was only one roll of toilet paper which ended up being a small issue toward the end of my stay. The location is great and the apartment was clean. I had no issues with the stairs or the size of the apartment, it was very typical for all other apartments I have stayed at in Europe.