Sarayburnu Park is a nice promenade by the Bosphorus, followed by the pretty Gülhane Park and a very nice place for a short stop while wandering around the Sultanahmet district.

You'll find an "Istanbul" sign here that you can take a picture with, as I did.

Book a hotel with a view of the Bosphorus

I just couldn't miss such a backdrop with the Bosphorus and the Galata Tower in the distance.

Sarayburnu Park

In addition, there is also a statue of Atatürk and a large flagpole with the Turkish flag in Sarayburn Park.

Sarayburnu Park is not a place you have to go to Istanbul for - but I would definitely walk from Topkapi Palace or Hagia Sophia Mosque just through Gülhane Park and Sarayburnu Park back to Eminönü Pier and the Egyptian Bazaar if the weather was nice.