I will try to answer this question thinking of what's visible over the surface. I think one of the first things you can observe is the sound of ezan (call for prayer) coming out of the mosques all over the city, five times a day. Other than its practical uses, I think it also serves as a mood setter. It brings a hush to the rush!
Aside from ezan, the prayer (namaz) itself especially on Fridays or during the month of Ramadan in the evenings becomes noticeable, as the crowds in mosques in the central neighborhoods spill onto the street with their seccades (small rugs used to pray on) covering parts of the sidewalk.
Month of Ramadan is perhaps one of those times where the Islam's influence in the daily life of Istanbulites is felt at its most. (Turkey uses Gregorian calendar.) During Ramadan, it could be hard to find a place at the restaurants at the time of sunset which is the time people who fast break their fast. Eating before this time is welcomed almost all over Istanbul, with the exception of some super conservative neighborhoods. On a seperate note, in general it's hard to find pork dishes in the city which is a direct influence of Islam.
Despite the modern face of the city, some neighborhoods tend to have a more strict dress code, especially Carsamba in Fatih ward would not be a pleasant place to hang out for someone who doesn't look like the rest of the people on the street. Other than very few such neighborhoods, almost all styles of Western clothing is worn and accepted in the city. Nudity, though may draw harsher response than it would in any other Western metropolis. This may be partially related to the Islam's influence but can't say for sure.
Istanbul hosts a large number of clubs, bars and other places where alcohol is served. But adult only shows -as in strip clubs- are quiet rare and if you happen to come across some, it would perhaps be at a dodgier place than its NYC counterparts.
As an American woman who lived in Istanbul for three years, I observed very little difference in day-to-day life between Istanbul and New York. The most obvious difference is the call to prayer, which sounds five times a day. It's absolutely beautiful but few people pay attention to it - don't expect to see people rolling out their prayer mats.
On the whole, most Turks I met consider themselves Muslims, just as most Americans consider themselves Christian: which is to say, aside from observing the holidays and maybe praying occasionally, there's very little outward expression of religiosity.
As an American woman who lived in Istanbul for three years, I observed very little difference in day-to-day life between Istanbul and New York. The most obvious difference is the call to prayer, which sounds five times a day. It's absolutely beautiful but few people pay attention to it - don't expect to see people rolling out their prayer mats.
On the whole, most Turks I met consider themselves Muslims, just as most Americans consider themselves Christian: which is to say, aside from observing the holidays and maybe praying occasionally, there's very little outward expression of religiosity.
