Of course, your number one reason to be in the province is to see the almost innumerable sights in Istanbul itself. When you have done them to your satisfaction, or just need to take some time away from the weight of history that defines the city, it's time to consider these outliers although it's impossible to fully escape from history here as well:
Belgrad Forest
Belgrad Ormanı northwest of Istanbul close to the Black Sea coast is named after a village now lying in ruins deep in the forest, founded by a band of Serbian settlers in 16th century from the namesake city. A mostly primordial forest with minimal human intervention, Belgrad Forest is dotted with Roman, Byzantine, and Ottoman aquaducts kemer; many of which were built by Sinan, the Ottoman architect of 16th century, which provided the city with fresh water, as well as small late Ottoman dams bent, many of which are accessible or at least can be seen from a distance in the case of aquaducts from the well-paved forest road between the villages of Bahçeköy and Kemerburgaz. Pedestrians pay 2 TL entrance fee, car drivers are charged with a somewhat higher amount. For transportation see Atatürk Arboretum.