Copenhagen Bound - Tips?

I was over the moon when Alexa from Lille Haus posted "What to do in Copenhagen" on her blog. If you're planning a visit to Copenhagen in the near future like I am, you should read what she has to say. Afterall, she once lived there.

I'm not sure how many decor8 readers have been to Copenhagen, but I need some help. I'll be there for a few days in early October to just hang out and see the sights. I've never been, so I'm looking for some suggestions - places to grab authentic Danish food, museums, historic landmarks, design-y type stores, etc. Also, I'm not sure if I should take a train from Hannover, Germany (where I'll be based) or if I should hop on a cheap flight.

If you could comment below with your suggestions, I'd really appreciate it. :) I'd ask you to email me, but I think it's better if you comment below so that decor8 readers planning their Danish adventure can also benefit from your fabulous tips.

Any globetrotters out there with some good Copenhagen must-sees?

Thank you so much!

(images from lille haus)