Our two favourite museums in Istanbul are the Chora Church Museum for its mosaics and the Archaeological Museum because we like looking at old historical artifacts.
Because it was raining heavily on the day we visited the archaelogical museum, we waited out the weather by spending our time imitating the posters of sculptures in the museum without the benefit of a tripod or good lighting; all but the last three black and white photos in this gallery are my attempts at replication them. The sarcophagi from Sidon were the most impressive artifacts in the museum.
The Chora Church museum is a little out of the way from the other sights in Istanbul but is well worth the side trip. The mosaics are richly detailed and we thoroughly enjoyed looking at them. Serene also enjoyed playing with the resident cats who are very friendly to visitors.