The Istanbul Archeological Museums hold outstanding collections of art from the ancient Near East, Greece and Rome.
When archeology became a science in the 19th century, most of the Near East was ruled by the Ottoman sultan, who got all the best stuff. These were his private collections, so they're pretty amazing.
The oldest stuff, in the Museum of the Ancient Near East, includes one-of-a-kind treasures like the tiled reliefs of lions and kings from the fabled gates of Ninevah, and the oldest written peace treaty ever discovered.