We’ve had a brilliant time in Oslo for a long weekend (DH is half Norwegian). We went in the summer so some of the attractions will be different but basically the highlights were:
Sommerpark or Winterpark (travel out of the city on the underground which turns into an overground train up in the hills. In summer, there was a large high ropes course, in winter skiing) - check it’s open for any activities you prefer.
Museums - there are a few very close together including the Viking boat museum, the Fram museum and a village type outdoor museum of Norse life.
Islands off Oslo - take a boat trip out
Sculpture Park (Vigeland)
Science museum
Trip to Holmenkollen Olympic ski jump
Additionally, we’ve travelled for longer and took the train up to Balustrand and the fjords which was great. We’ve also travelled up to the Lofoten Islands which are incredible but a long way away. We flew up and got an overnight train back (not all the way to Oslo though, if I remember rightly).
It is expensive in Oslo but a great city break if that interests you.