hi, efmach. We spent a few days in Denmark this summer on the end of a holiday in Sweden - we drove via Malmo across the enormous bridge to Copenhagen, had a whole day in Copenhagen which is lovely (but almost impossible to get out of, the road signs are rubbish, they must want you to stay) and then drove about halfway across. The countryside along the way was a bit flat and boring.
We then camped (so no help there) for 2 nights and spent the middle day at Legoland, Billund which is fabulous. It helped that the weather was perfect, and also that it was the 3rd week of August when Scandinavian children have gone back to school so it wasn't too crowded, but it was one of the best days out we have ever had - our 2 boys (14 and 9) had a marvellous time. I didn't hear a single child crying all day, there was no litter and the meal we had at one of the restaurants (Pizza and Pasta I think) was superb.
We travelled to Sweden with the car on DFDS ferries, 24 hours each way, which was a nice way to start and finish, but I think if you flew with eg Ryanair and then hired a car it would probably be cheaper.
As Rosie says they are dead keen on environmental issues and, for example, in Copenhagen bikes are everywhere and even take priority over pedestrians apparently (ie I was nearly knocked down by one crossing on a green light!)