It is incredible that such a beautiful natural area is so close to the city and so easy to get to. The T-bane to Frognerseteren takes you up in under 30 minutes with some amazing views on the way. A normal zone 1 ticket, either single of 24 hours will get you up there. Then you have a lovely walk through the woods, maybe stopping at the Frognerseteren restaurant for some Eplekake and hot chocolate before taking a walk down to Holmenkollen to see the ski jump. There are T-Bane stops all the way down if you want to jump on earlier and head back to the city.
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