Try the FS Sultanahmet
We were just in Istanbul Easter week, stayed at the TomTom Suites 2 nights and then the FS Sultanahmet, which we really enjoyed. We had the least expensive room: overlooked an "archaeological site" but also the Hagia Sofia which was great.
People were wonderful, the courtyard was full of tulips, delicious b'fast and it is close to all the sights. From their roof top restaurant you can get great views, though they were just opening it up when we were there.