This UNESCO World Heritage Site is the burial place for numerous Danish monarchs since the 15th century. Constructed during the 12th and 13th centuries, it is the first Gothic cathedral built of brick and encouraged the spread of its Brick Gothic style throughout Northern Europe.
Located just 25 mins outside of Copenhagen by train, the cathedral is easily accessible on foot from the train station. I was severely under the weather when I visited, and it took all my strength and determination to leave my hibernation-like state from the hotel to make my way here. There's probably a few other sites to see in the area, but this is the main one.
If your time in Copenhagen is limited, I would recommend you spend the time to visit Kronborg castle first. Unfortunately the train lines don't exactly overlap for seeing these two sites, but there's plenty of other things to see when walking around Copenhagen.
A beautifully maintained cathedral, and also a UNESCO World Heritage Site.