Istanbul is a city of contrasts. It's a city that's both modern and ancient, where great restaurants, hopping nightlife, and horrific traffic exist alongside some of the world's most impressive ancient wonders. It's both western and eastern, culturally as well as geographically: It's the only city in the world on two continents (Europe and Asia). A visitor can listen to the Muslim call to prayer while standing in the shadow of the Blue Mosque and feel transported to another time -- or go clubbing after nightfall with Istanbul's trendy urbanites. Though Istanbul is predominately Muslim, there's a clear divide between the secular, westernized population and the conservative Muslims: as a result, it's not unusual to see women in chic western dress alongside women in burqas. And a smattering of other faiths also call Istanbul home, including Greek Orthodox Christians and Jews (European Jews first sought refuge in Istanbul during the Inquisition).
The Turks are famous for their hospitality, and tourists, including Americans, should feel very welcome here. Though it's good to be cautious in any large city, Istanbul's crime rates are relatively low and most tourists won't have much to worry about aside from getting occasionally overcharged by taxi drivers.
Most tourists will find themselves choosing between two neighborhoods: Sultanahmet (the Old City), or Beyoglu. Sultanahmet is where tourists will find historic attractions such as the Hagia Sophia, Blue Mosque, Basilica Cistern, and Grand Bazaar, while Beyoglu is home to the city's best restaurants, nightlife, and shopping. There is convenient tram service connecting the two areas (separated by the Golden Horn), and taxis are cheap. (Ask your hotel to call a taxi rather than hailing one form the street to avoid scams.)