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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It's easy to miss the Hippodrome, in a sense, because it's the space between buildings. It's well worth paying attention to, though.

The space still retains the long shape of the chariot racing track which was famous in antiquity and was the site of a famous riot. The fans of the racing teams were as obsessed as modern day football fans.

In the centre, the late Roman and Byzantine emperors displayed numerous antiquities hauled to Constantinople from all over the empire, including Egyptian obelisks and the serpent column from the sanctuary of Delphi in Greece, which was set up to commemorate victory over the Persians by the Greeks in 480 BC. Only the column is there now, but it used to support a giant tripod (bowl on three legs) - a fitting symbol to put in the Hippodrome since tripods were, like modern 'cups', the usual prize in athletic games.

The Egyptian obelisk is from Karnak, brought to Constantinople by Theodosius I, and placed on a relief-decorated base. The base shows the imperial court and Hippodrome scenes, and around it is the original ground level of the Hippodrome.

The Hippodrome is between the Blue Mosque and the Museum of Islamic Art. A row of tea shops next to the Blue Mosque looks onto it

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A high hill on the Asian side of the city, it's lovely to take a taxi to the park up here at sunset to watch the sun go down over the city, see the Bosphorus bridge and the city light up, and hear the prayer calls from all over the city come up from all around you - your very own surround sound system.

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