Hello G-ARVE
We stayed at Hilton, walked to Taksim square, around 10 minutes, took fenicular railway to Tram 1, then tram 1 to blue mosque etc, around 40 minutes total. Other way is to Taksim square, then the old tram and then the old fenicular down to river and walk or tram from there, around 1 hour.
Hilton nice hotel, but awful issues with noise if you are on river facing room from nightclub across road, which Hilton are in legal fight with to get them to stop music are set hour, out of 4 nights, we had noise 3 night till past 0200