The shopping in Copenhagen is fantastic! They have a bunch of high end stores, but what I really liked were the smaller shops. I found a shoe shop called Scarpa. They specialize in leather shoes designed in Denmark but made in Italy. The sales gal told me I would only find them there, so I was sold. I bought a pair for 30% off and love them!
TL and I also enjoyed the microbreweries in Copenhagen. Different spots near the water sold really good beer that we enjoyed. There is a lot to see and explore in this city - and we did the best we could in the 3 days we were there.
One of the must sees (although it's tiny) is the Little Mermaid. It's one of the most photographed sculptures in the world.
Copenhagen is beautiful... if you're visiting the Nordic Countries, it's definitely worth a visit, even if just for a day!