We have spent three days in Pashas house. It was a great time. The apartment is clean, there are everything you need for a short stay, including towels, an iron, a hair dryer and a kettle. If you go out, you can buy cheap fresh fruits, eat something and buy baklava. During our stay we walked through the different parts of the city and we didn't face any problems with the public transport. The metro and bus station are in 15-minute walking distance , but this was completely fine for us. Istanbul never sleeps, but it was quiet at night.
If you want to stay in Fatih or Sultanahmet, i completely recommend you to book the Pashas house.