Hillerød is a fairly large town in Northern Zealand. It is less than an hour by train from central Copenhagen so it is easy to go here on a day trip if you are already visiting Copenhagen. You can just take the S-train line A Hillerød is the last station on the line heading north of Copenhagen.
The city is small so you can easily go around the old part of the city on a short walk. There are some nice older buildings in the vicinity of the station you can go around and have a little look at.
The main attraction of the city is the large Frederiksborg Castle close to the central station. Around the castle is a large garden which you can go inside and visit for free. But the main highlight is the castle which is also a National Historical museum of Denmark – even if you are not interested in Danish history the castle is still well worth a visit so you could go inside and have a look around.
After you have visited the castle you can take the local train further north. It will lead you to a small station from where you can bike along the road to an old monastery called Esrum Kloster. It is nice area with an old monastery which doesn’t have a lot of tourist so you can go and enjoy it if you like. It is possible to take a local bus as well but it will take longer.
You can also take this local train line all the way to Helsingør where you can go and visit the other famous castle of northern Zealand – Kronborg Castle or the castle of Hamlet.