Istanbul — the provincial capital, where 95%+ of the population of the province resides
Ağva — at the far northeast of the province on the Black Sea, with charming guesthouses lining the banks of an emerald river
Polonezköy — a village in the backyard of Istanbul founded by Polish settlers in 19th century, with pleasant traditional houses and beautiful forests
Princes’ Islands — nine car-free islands off the southern coast of Istanbul; pine forests and impressive mansions are the main features
Şile — town on Black Sea coast northeast of Istanbul; a favourite location for swimming in weekends
Istanbul Province basically extends over two peninsulas surrounded by Black Sea, Bosphorus, and the Sea of Marmara—Çatalca to the west of Bosphorus on European mainland and Kocaeli to the east of Bosphorus on Asian mainland.
Since 2005, Istanbul Province is officially co-terminous with the city of Istanbul, as the city borders were extended to include everything within provincial borders, but whatever official designations say, other than the huge metropolitan area—in a triangular shape, which has its base on the Marmara coast, covering an area up to 25-30 km long from the southern mouth of Bosphorus at each side, with the height of the triangle going all the way to Black Sea along the Bosphorus—the rest of the province is rural, or at least suburban, in character.
On Çatalca Peninsula, geographically an extension of Thrace, a continuous conurbation formed by summer houses of Istanbulites—concrete cottages in usually densely packed, albeit somewhat leafy, housing estates, which people of the crowded city flee in every possible opportunity, which makes highways west of city highly congested on Sunday evenings in summertime—lines the southwestern coasts along Marmara. Inland is mostly open farmlands producing much wheat and sunflower, and dotted by villages, although landscapes get more industrial as you get closer to the major highways or the outskirts of Istanbul. The vegetation gets lusher as you approach Black Sea coast, although some of the forests close to the shore are pierced by ugly open pit-mines. Another feauture along Çatalca's Black Sea coast is quite large Lake Terkos (Terkos Gölü, a.k.a. Durusu Gölü), a freshwater lake although seperated from brackish Black Sea only by a series of dunes and one of the major sources of drinking water of Istanbul.
On the Marmara coast of Kocaeli Peninsula, the city of Istanbul proper well extends to (and beyond) the provincial border. Inland of this peninsula is more verdant than Çatalca, with some of the hills (around Alemdağ) covered by heathlands, a rare habitat that is found only in a handful of locations across the World naturally. The Black Sea coast of this half of the province is also wooded, but again just like its counterpart to west, is cut through by open-pit mines at several locations.
Virtually among all options of getting into the province, you will have to touch down Istanbul first in one way or another, although it is generally possible to get off the buses heading for Istanbul from locations in Eastern Thrace in Silivri, around 60 km west of Istanbul.
Anastasian Wall (Anastasius Suru, a.k.a. Long Wall of Thrace; not to be confused with Theodosian Walls of Istanbul proper) is an ancient defence network built by Byzantines to stop barbarian raids onto the imperial capital from west, that is comparable to Hadrian's Wall of Britain in size (but certainly not in popularity!). While most of the actual walls, which once stretched for 56 km between the coasts of the Black Sea and the Sea of Marmara, i.e. along the entire width of Çatalca Peninsula, some 60 km west of Istanbul (the southern end of the walls are thought to be in Silivri), were re-used in some other constructions through the ages, it is very much possible to see some fairly well preserved sections in the woodlands to the north, but you'll need a very detailed map of village roads beforehand.
While the alternatives for your next destination is limitless thanks to flights from Istanbul's Atatürk Airport to all six inhabited continents, here are some of the closer destinations:
Eastern Thrace to west, geographically European and culturally Balkan part of the country. Close to the borders of Istanbul Province are Kıyıköy and Vize on the Black Sea, to the northwest of the province, which may be combined with a trip to Lake Terkos, and who knows, maybe with some exploring along Anastasian Wall.
The beautiful city of Edirne, a former Ottoman capital lies further afield towards northwest. Tekirdağ to west is a pleasant coastal town noted for its local meatballs and raki; and highway leading to which is lined with the extension of summer houses conurbation of southwestern Istanbul Province.
To east, Eastern Marmara lies. Sapanca is a pleasant lakeside town about two to two and a half hours away by frequent trains. If you happen to take the coastal road from Ağva in the northeast, Kefken—which has highly scenic beaches and forests—is the next town on your itinerary.