We had a great time in Istanbul, Thank you!
The apartment's location is very nice. We had a little grocery store, an exchange office, a coffee shop (with both Turkish and espresso cafe) in 20 meters. In 100 meters you can find almost anything you may need. The sightseeing spots can be reached with ~15 minute walk, in every direction.
About the security: the overall security feeling was more than great during our stay. I had nothing to fear from when I went to run at 10pm. On the touristic places, big malls, public transport stations you can see policemen with heavy weapons. But we had no issues about it. So do not allow your fear make you stay at home :-)