Québec City will offer the most european experience, with a lot of history. It is truly a beautiful city.

Montréal offers more to do, and a better compromise between North America and Europe. If the OP doesn't speak French, he/she may be better off in Montréal.

Either of the two Québec cities would be my suggestion. Toronto and Ottawa aren't that different from any American city.

Really? And does LA = Detroit = Miami = Honolulu?

If you're from Oslo, I suspect that you're familiar with European cities. If you want something different, then I would vote for Vancouver. Yes the flight is a bit longer but once you deal with all the airport hassles, what's another hour or so in the air. Vancouver has a vibrant mix of Asian influences and west-coast laid-back attitude, wrapped up in a lively urban environment with stunning scenery consisting of water, mountains and a rainforest (Stanley Park) adjacent to the most densely populated part of Canada.

I grew up on the Canadian prairies and always have enjoyed visiting Vancouver whether for work or pleasure. Now that I live in Texas, I wish it was as close as it used to be.

If you opt for Vancouver, stay in the Robson street area which is walking distance to cool shops, great food, Stanley Park and the harbour.

When are you coming to North America?
If it is in August then you can pick any city that has been mentioned - I am not biased - depending on whether you like a big city or you would like to explore outside these cities.

If you are coming in September I will give Quebec city a try - you can go further east towards Baie St Paul and explore a bit the northern part of the St Lawrence river and even visit ile d'Orleans whilst you are in Quebec. Vancouver will be my other choice .