Okay, so if you've been doing your research, you have probably come to realize by now that Istanbul is a city that is near peerless when it comes to culture and history. Then again, said research may also have led you to believe that there is a true scarcity of adventures available within proximity to this overwhelming metropolis. Sadly, it's true. Case in point: the nearest mountain worth ascending and/or skiing on is the mighty Uludağ, a daunting five hour drive around the Sea of Marmara. Scuba divers may need to travel all the way to the opposite end Marmara to destinations like Saros Bay, Gallipoli, and Gökçeada, all of which will take a good four hours of driving. Even skydivers are better suited flying out to the nearest drop zone, a whopping 600 km away in Ephesus. Which isn't to say the Embark traveler can't find something beyond the din of the bazaar or the simple reprieve of the hamam, you just may have to look a bit harder than usual.
There are a few options within proximity of the city for stretching your legs in the natural world. Belgrad Forest, just north of the city, is the premiere option for short hikes and a scattering of mountain biking trails. Just north of this is the Black Sea coast, where some of the few well-kept stretches of beach in the region are located. The resort towns of Kilyos and Şile are your best options for maintained beaches, while the cliffs of nearby Ağva provide a superlative backdrop for a handful of coastal hikes.
If you're willing to head outside of the Istanbul bubble, there are a number of enticing options for all manners of adventurer. Heading west, the small city of Tekirdağ is home to some of the Sea of Marmara's best beaches, while nearby Mount Ganos is a perfect day hike. Further north in Kirklareli is the most intriguing cave in the region, the massive, three-chambered Dupisna. Much of the coast along the sea in both directions is actually quite industrialized and underdeveloped, meaning that you may have to do some real searching to find anywhere else worth enjoying the water. As for hiking, there are a smattering of options in small, localized natural areas, while hikes like the one to the Erikli Waterfall near Cinarcik, those in the Inonu Valley near Ismit, and the hike to and through Ayvaini Cave near Bursa are all worth a day trip or overnight stay if you're up for something a bit more exciting than the usual tourist agenda.
For further information, browse the included links; and don't be afraid to make your stay in Istanbul more of an adventure!