Housed in a glorious Victorian Mughal-Gothic hall across the tracks from the Old City, the Peshawar Museum has the largest collection of Gandharan art in the world, ranging from statues and friezes depicting the Buddha's life to winged cupids and Herculean heroes. It's a dizzying stylebook of Graeco-Bactrian art, if often let down by poor labelling (also check out the Graeco-Bactrian coinage hidden upstairs).
There's a small Islamic collection with some delightful illustrated books, and an ethnographic section with wooden effigies taken from a Kalasha cemetery, including an ancestor figure riding a two-headed horse.