Me and my girlfriend highly recommend BeyazıtHan Suites! They're so kind, gave us many advices and helped us in many occasions.
The location is simply perfect! 5 minutes of walk from many tourist attracions (such as Grand Bazaar), restaurants, shops and tram station to reach any place you want and need.
The apartment has everything you need, even if you want to cook your own meals, is clean (every morning a lady will do the cleaning) and is super quiet at night.