Local in North Zealand
If you’re looking for free fun, there are a number of local options in North Zealand – you can go for a walk in or around the area:
Frederikssund Viking settlement
There is also Esrum Lake in Gribskov, Aboretet in Hørsholm, Russia at Dronningmølle, the many beaches along the coast, the ramparts and fortifications of Kronborg and the Nordkyststien cycle route.
At Visit Nordsjælland you can get a good overview of many more possibilities:
Free joys in Copenhagen
If you fancy popping into Copenhagen, there are plenty of free things to do there too, including
Know your Bro – digital city walk in the bridge districts of Copenhagen
Look at architecture – in Copenhagen