If you're searching for a sense of wilderness in the midst of Istanbul's great mosques, lively bazaars, and cramped dolmuş rides, then your nearest and dearest opportunity would be Belgrad Forest. Just northwest of the city, this 55,000 hectare proliferation of protected woodland provides plenty of hiking, mountain biking, and summer shade for when the days are hot and the thought of a crowded beach makes you squirm.
A very popular area for barbecues, with numerous picnic spots and even an on-site cafe, you'll find Belgrad (Belgrade in English) to be a place of both leisure and activity. There is a 6 km footpath that surrounds a central lake that is a favorite for runners, while there are also a number of unmarked trails that are a rare opportunity for mountain bikers in this metropolis of 17 million people. If you're up for little exploring, there's a massive aqueduct near the road that used to be an Ottoman water supply system that led all the way to Taksim Square, while you'll also encounter the scattered remains of a community formed hundreds of years ago by displaced Serbians from the city of Belgrade.
Getting to and from the forest may be a little tough if you don't have a rental car; a cab ride is decently cheap from Haciosman, while buses depart from various points in Istanbul to Bahcekoy, which is a moderate walk from the park entrance. Check out the included informational links for more.