A wonderful way to pass a few (or even many) hours in Istanbul, is going to Gülhane Park. Gül means "rose" in Turkish, so the name of the park means rosehouse park. The flower arrangements are lovely, but what I valued the most was the shadow from the old trees, especially the tall plane trees. They help you escape the hot summer days and the hustle and bustle from the Sultanahmet or Eminonu area. The tranquility is wonderful for a city like Istanbul, where you can never hide from agitation.
This park was originally part of the outer garden of the Topkapi Palace, and was open as a park to the public in 1912 for the first time.
If you slowly walk uphill around the exterior wall of Topkapi Gardens, you will see a gate which leads towards the castle. And close-by a simple coffee and tea house with one of the best views of the Bosphorus which I had. This was the best place to find tranquility in the oh-so-busy-and-loud Istanbul. It was the place where I found peace and enjoyed everything that was happening to me. So why don't you take a walk up there as well.