After a large breakfast to make up for the lack of sleep I headed out to the station. My first stop for the day was to be Frederiksborg Slot in Hillerød. I got to the station and purchased my ticket only to find that there were engineering works and I had to get a rail replacement bus part of the way (I thought I was in Denmark not Britain!)
Thankfully everything worked and, although it took a little longer, I got to Hillerød just before midday and wandered down to the castle.
After having had a look around I decided, rather than trying to repeat the journey back I would go on to Helsingør (only about 20 minutes by train), have a look around the town there, and then head back into Copenhagen by direct train from there.
By the time I got back to Copenhagen the weather had pretty much cleared up for the evening, and after having had a wander around the town for a bit I headed over to Nyhavn to pick up one of the canal tours that run from there.
After the tour I then took the extended tour using one of the waterbuses that now run up and down the harbour and are included on the city tickets.
By the time I got back to Nyhavn it was getting late so I grabbed a bit to eat and then headed back to the hotel, hoping for a better night's sleep.
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