An idea just occured to me - if you are interested in military stuff and military history.
If I recall properly, the Historical Collection on the Royal Guard base in Copenhagen is open to the public on Wednesdays - which means that anyone can pretty much just be admitted to the grounds of the base if they ask. This is of course the base close by N$rreport Station, and right across from the Botanical Gardens and the Geological Museum. You know, the base right next to Rosenborg palace (where the Crown Jewels are kept).
If you have the time, go to the main entrance to the base (Gothersgade), on Wednesday, and tell the guard that you are going to see the Historical Museum (called "Historisk Samling"). He
should admit you to the base (and give you directions). If you time it right - right before 11:00 AM - you'll get to see the palace guard prepare for the guard change, and leave the base. If it is a full guard change (i.e. the queen is in residency) they will be starting to get ready by 11:00 AM, and will leave the base around 11:30 AM. If it is a smaller guard change, they'll leave slightly later (and will be less impressive, with no marching band, and only a small detachment).
If that kind of thing interests you, it might be a lot of fun to actually be on the base and see the guards line up, be inspected, be issued ammo, etc - and then leave for the guard change. Most people of course do not realize that you can actually get onto the base on Wednesdays.
(Of course - it is POSSIBLE that they have since changed it, and you will not be able to get on the base, but I doubt it. If you try, and I was wrong, then I'll owe you a cold Tuborg
)
The Historical Museum, in addition to being a pretext to get onto the base, is also quite nice - even though it is small. Also, you should see my picture somewhere on the wall, since I believe they still have the pictures of all the officers who ever served in the regiment displayed.