Belgrade Forest (Belgrad ormanı) is a large green area to the north of the city. It has many entrances but I recommend the one at Bahçeköy which is closest to Neşet Suyu, where there is a 6km path/track around a lake. Here you can walk/run in the fresh air and then enjoy a snack at one of the little cafes near the start. The area is very busy at weekends in the summer for barbecues so I would recommend a visit in midweek or in the off peak seasons.

It is lovely to be only 20km from the centre of the city and yet only hear birds.
It is possible to explore further, but signposts tend to be Turkish only, which could be awkward! It costs 5 lira for a car to enter the forest or 1 lira for someone on foot.

Getting there is the problem!
The 42T bus from Taksim will take you to Bahçeköy and from there it is a very short walk to the entrance.
Alternatively a minibus from Beşiktaş towards Sariyer passes the Kilyos turning to Bahçeköy and people frequently pick up hitch hikers from this corner. (I must point out that this is not a good idea for women on their own).
Unfortunately from the entrance it is then a further 2 km to Neşet suyu which would tire out smaller children.
Ideally you need some sort of personal transport or a reliable taxi service to make the journey easier. A taxi from 4. Levent (the last stop on the metro from Taksim) will cost about 25 lira one-way (a tenner) which is very good for four people.

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