I was in Istanbul over Christmas of 2003... and the arrival tax was the whopping $100. However, I just took the hit on the chin and enjoyed my stay anyway. I found everything else was a good enough value that I could offset the ridiculous visa cost. We stayed at the Empress Zoe (on recommendation from FT) which is in your price range, and literally in the shadow of the lovely Hagia Sophia.

As I recall, a nice, fun dinner at the trendy "Vogue" was only $100 for four people including sushi appetisers, a few glasses of passable Turkish wine, and dessert.