Tromsø museum (University of Tromsø),   Bergen Museum (University of Bergen),  Mineralogy-Geology and Paleontology Museums (University of  Oslo) all have excellent geology exhibits.
Vitenskapsmuseum (NTNU)  has no geologist or geology exhibit, but has a nice little mineral exhibit that inspires many visitors.

The doors are open to the public five days a week, from  8 to 15.45,  and the exhibit is free.
(But don't get a parking ticket: there is almost no guest parking available at Gløshaugen!)

The exhibit is 70 m².

It includes:

• 12m²  prydsteinsvegg (rock display wall)  with 150 identified samples of Norwegian rocks, with an identification map.

•  23  display shelves  with over 650 museum samples: silver, gold, crystals, minerals, fossils, meteorites.

Meteorites, including a Norwegian meteorite that fell on Tromøy i Aust Agder i 1950.
Silver crystals from the historic Kongsberg silver mine (thread-silver, plate-silver, moss-silver, etc..)
Gold-bearing rock from Australia
Dinosaur egg and fragments of  large dinosaur bone from the south of France
Jurassic leaf fossils from the bottom of Beitstadsfjorden (Trondheimsfjorden).    Did Jurassic dinosaurs eat such plants?
Shell fossils, 10 000 years old.  Fossils like these can be collected many places in the Trondheim area.
Important Norwegian geological resources through the years, such as:
    Kongsberg silver
    Trønder copper ore from the historic Røros and Løkken mines
    North-sea oil.
    Polished Norwegian rocks (trondhjemite, larvikite, Fauske marble, Otta slate, etc.)