One of my favorites places in Copenhagen. When you will reach the top you will have amazing view to the city. And going up was great experiences.
Go to this church for some of the best views in Copenhagen, stretching across the city and down to the Øresund Bridge. Climbing up the spire (literally around the outside of the spire) is perhaps not for you if you're afraid of heights - it does feel a bit precarious. For everyone else - do it. It's really fun and absolutely beautiful.
be sure to go on the OUTSIDE stair on the spire (top) of the church. Not for those afraid of heights ;-)
Denmark is flat, and this could possibly be the highest you can get (not counting the Freetown next door..). The views from the top are definitely worth the price of admission! It gets quite wobbly in high winds (always?) which only adds to the attraction..
Vor Freslers Kirke, or Our Savior's Church, is fantastic! You can catch Wednesday evening or Sunday organ concerts. Even when it's not playing however the ornamental pipes alone are breathtaking. The Church’s highlight though is the spire, a quintessential piece of the city skyline. You can walk up the lined spiral stairs on the outside of the tower and the top offer one of the best views of Copenhagen. It closes down on windy and rainy days and usually a bit early in winter since the sun sets so early, but it is worth the hike up every step to see the city's red roof's and waterways. It is easy to get to by bike or located just a block or so from the Christianshavn Metro.