We would totally suggest staying in Besiktas as the neighborhood atmosphere is amazing and local (especially at night) and it's also very easy to move around. The flat is in the heart of the area with many bars and restaurants just a minute walking away but in a quiet street so you don't have any trouble to sleep. The host was extremely nice and even took time to show us around when we arrived, showing us where to take public transportation and showing us bars and places to eat he liked!