If you are a fan of the Danish political drama Borgen then this place is probably at the top of your list. The building itself is very impressive and the parade grounds on the southern edge are a great place to wander and get some photos. There are free tours run of the Parliament (check online for details) and they are first come first served so it is good to book in advance. The tours are excellent, run by knowledgeable and entertaining guides. If you are lucky then you may get introduced to some of the politicians wandering the corridors as we did.
One of my favourite places in Copenhagen! For about USD20, I toured the palace ground on my own. Felt like I stepped into a Disney movie. Ha! Rich in colour & history. Ballrooms to personal libraries to throne rooms to dinner halls to tapestry & china. Tour of the royal stables included! all the carriages, brilliant! definitely recommend a visit to Christiansborg.