West of town (1.5km), this extensive open-air museum includes 18th- and 19th-century buildings, a local folk-history exhibit featuring the creepy Devil's Finger (a finger cast in pewter of unknown origin, but which is said to have caused a number of deaths when it was removed from the church), the ruins of the castle, and the extraordinary showcase 'glass cathedral' (Domkirkeodden), which dominated Hamar until 1567, when it was sacked by the Swedes.
The grounds themselves are free to visit and open all the time and you can also peer through the glass-house–like structure that surrounds the ruined cathedral but to get inside this or any of the other museum exhibit buildings you'll need a ticket.
It's a pleasant walk or cycle from town along the lake shore to the museum.