Visit Oslo Camping in Møllergata for beer and crazy golf. Good times. For nice nature walks or skiing, you can take the subway or local trains to Nordmarka, Østmarka or Lillomarka. Holmenkollbanen to Frognerseteren, T-banen (subway) to Skullerud or bus 56 to Solemskogen. There'll be a Christmas market in Spikersuppa, between Stortinget (Parliament) and the Royal Castle.
Sorry to hear about the veganism, can't help you there - have you seen a specialist? 😆