Getting around North Zealand is easy
It is very easy to get around North Zealand on your own using the public transport system. There are S-trains to Hillerød (lines A or E) every 10 mins. during the day.
Hillerød and the Frederiksborg Palace
From the station in Hillerød it is only about 15 mins. walk to the majestic Frederiksborg Palace in the centre of town. Hillerød in itself is well worth a visit, a very lively and busy town with a friendly atmosphere. From Hillerød there is a direct train connection to Elsinore (Helsingør).
Count on spending an entire day doing this trip of North Zealand.
The Copenhagen Card
The CPH Card is definitely worth considering as it covers all public transport and entitles you to free or discounted admission to many of the sights.
The CPH Card is available from the Visitors Centre, hotels and major train stations.