The Bistrița-Năsăud County Museum, housed in a 16th-century guildhall building on Strada Gen. Grigore Bălan, runs through the region from prehistoric times to the 20th century. Strong sections on the Dacian and Roman periods, the Saxon settlement of the area, and the rural folk culture of the surrounding mountains.
It is small and not very modern but a useful primer on why Bistrița looks the way it does. Captions are mostly in Romanian; ask at the desk for the printed English summary.