Re: Europe travel question
Yes Duncan, Copenhagen is my favourite European "chill" city. I love low rise cities!
Grea, my personal opinion is that a week (i.e. 6 days + 1 day travel) is a bit much, unless absolute relaxation is foremost. Circa 4 days (+ 1 day travelling) is a more stimulating schedule IMO. Maybe consider (especially if you're thinking of travelling by train) stopping over at a few smaller towns in each of your target countries or passing through. That way, you'll get to experience something closer to the real culture of that country, rather than just the capital city stuff. Often much cheaper too, as well as offering variety.
If you're settled on the main choices of Amsterdam, Vienna, Paris, & Rome, then also consider Milan, Monaco, etc. BTW, there's a great fast train service between Amsterdam & Paris called Thalys (Google it).