Denmark is the home of Lego and if you're traveling with kids in Copenhagen, it shouldn't be missed. It's located along the Stroget -- the pedestrian shopping district in the city center of Copenhagen. You can either split up with one adult takes the kids to Lego and the other can browse the other interesting shops or you can do it all together (we held the Lego store out as a carrot to keep the kids engaged and in check).
Flagship Lego stores have exclusive Lego sets that you can't find elsewhere. There are also building stations and a fascinating video monitor that will bring a set to 3-D life if you hold the box in front of the camera. They also have a huge pick-a-brick wall where you can pick up missing pieces or just get creative.