If you have more than a few days, I recommend taking the ferry to one or more of the Princes' Islands.
There are no cars, hardly any other city life noises and the air is definitely cleaner. They are my favourite spot for peace and quiet especially in winter, early spring and autumn as there is hardly anyone visiting and the beautiful wood-clad houses from late 19th century are empty and serene in all their glory.
You can walk around or take a tour in a horse drawn open (covered in winter) carriage and have a glass of tea by the port.
There are regular ferry services to the islands from Eminonu on the Golden Horn and Bostanci on the Anatolian side
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Buyukada is the largest and furthest out. It's also the one worth spending the most time on. At the southern end is a high hill with St George's monastery. It's a long treck, but well worth it for spectacular views over the Marmara sea. In addition, you get to look for Trotsky's house on the way.
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