If you're looking for a place that is central to the traditional tourist attractions (Ayasophia, Blue Mosque, Grand Bazaar, Topkapi palace, etc.) then this is the spot. It is a 5 minute walk to the Gran Bazaar and Sultanahmet square, and even shorter walk to the the train. There is a small market literally across the building that has most of what you'll need and three larger supermarket chains just a short walk from there.
There is plenty of restaurants with food close by, but if you want my advice I'd venture out of Sultanahmet altogether to get good food. It is difficult to find good quality food in the main tourist hubs.
The apartment comes with all the basic necessities and is otherwise pretty comfortable. I was there with my 18 month old and it was convenient for her.
The best part of the apartment is Ugur, who is there to help you with anything you need. He'll meet you once you come in and is a phone call away from any help. He even brought us a basket of toys for my daughter. He can set up pick up and drop off from the airport for you for extra charge, and gives you a cell phone (not smart phone) for your convenience as well. There is a house cleaner who cleans the house and changes towels every other day as well. So I think overall it is a good spot and we enjoyed ourselves.