Denmark is awesome and I hit my head.

Old seems to take on new meaning in Europe, for Americans anyway...

You got that right! A few years ago I had the chance to go to Crete on business for 10 days. The only time I was needed for work was the 2nd and 9th days of the trip so the rest of the time my wife and I played "tourist". It was amazing to see old Greek ruins that were built on top of older Roman ruins that were built on top of even older Greek ruins. The ruins of the Palace of Minos at Knossos was incredible - and to think it was completed about 1900 B.C. boggles the mind.
We had a long layover in Athens on our return and I was fortunate to be able to book a half-day tour in a private Mercedes taxi with a guy who lived in New York for over 20 years. He took us to the Acropolis and other ancient sites in Athens that I could have spent days at. I told him that, as Americans, it's difficult to fathom the age and history of those ancient cultures since the oldest things we have in America are trees (the Redwoods, Sequoias and Bristlecone pines here in California).
Enjoy your trip and see as much as possible!