If you have any interest in trains, this is worth a stop. The Norwegian Railway Museum was founded in 1896, making it one of the oldest transport museums in the world. It sits on the shore of Mjøsa, about a kilometre north of Domkirkeodden.
The main building covers Norwegian railway history from the very beginning. You can climb into old passenger carriages, see how a signal box worked, and watch model trains run through dioramas as you walk past. Upstairs there are scale models of every locomotive type that ever ran in Norway.
The outdoor park has two locomotive halls and several historic railway buildings. The centrepiece is Dovregubben - Norway's most powerful steam locomotive, a Type 49c built in 1940. It pulled express trains over the Dovre mountains between Oslo and Trondheim until 1958. The name means "The Mountain King" from Ibsen's Peer Gynt. It was Northern Europe's largest and strongest locomotive in its day.
During summer, you can ride two narrow-gauge trains through the park: the children's train Knertitten and the working steam engine Urskog.
The museum also runs heritage train tours on the main railway network. Their Stålvogntog - vintage steel carriages pulled by a classic diesel locomotive - goes to Røros for the Christmas market in December, to Grundsetmart'n, along the Rauma line to Åndalsnes, and various other destinations. Check their website for upcoming trips - they sell out quickly.
The museum is open year-round, Tuesday to Sunday, though some outdoor sections close outside summer.
The first weekend of November there's a large model railway exhibition - worth knowing if you're visiting Norway then, as November is generally a quiet month with not much else happening for tourists.