A wonderful museum, that wasn't busy at all -- perhaps because we went at 6pm (not deliberately but because we had had a full day. That day it was open until 9!). The comparison with the V&A is irresistable.
The collection covers a variety of cultural artifacts -- carpets, clothing, room interiors, pottery, jewellery etc. My favourite exhibit was the shadow puppets, which includes a film of a performance including the background to the art. The building is also fascinating.
If your guidebook says that all government-run museums in the country close on Mondays, well this one doesn't. It is poorly signposted but is right next to the Hagio Sophia History & Experience Museum (not the church!)