Overall, Istanbul is just like any other large city in regards to safety. You need to take the same precautions in Istanbul that you would in New York or London.
You can visit Blue mosque, take a walk along the Bosphorus or go to luxery shpo centers as Istinye Park or Ak Merkez. There are more then 10m people so you may not get bored.
There are many historical sites to visit including palaces like the Dolmabace and the Topkapi. The Princes Islands make a day's visit. There is the Bazaar, the Beyazit Tower and Istiklal Street as...