Cindy W.
Yelp
Rosenborg, Christianborg...then Frederiksborg Sløt, and that's the order of impressiveness, by Frederiksborg wins by far. It's a wonderful day trip, be sure to take note of my protip later.
TRAVELING
Take the train to Hillerød (depending on where you are, you are traveling a lot of zones. Up until they stop circulating the clipcards, or klipkorts, get the 10-clip 5-zone passes). We started at central and got on. You get out of the station, go straight, pass a cemetary, take a right, and then left when the road forks. Continue on and then you'll come into a little cutesy town square. Walk down it until you hit the lake, and then circle right and wind towards the castle.
Admission is 60DKK for students, 75DKK for adults. There's a national history museum inside with regards to the royal family with tons of portraits, and various artifacts (the most beautiful ones are the clocks and astrological globes...HNNGGG).
Wear comfortable walking shoes and clothes, because there are pebbles and cobblestones everywhere.
PROTIP
Always check weather first. Pack a lunch and sit on the amazing grass after winding through the gardens and looking at the lake. Bonus if you pack cards, booze, and a mini speakerbox. This was one of the reasons why I began to like Copenhagen.