Need a change from the city? Then you should consider jumping on Kystbanen, which runs from Central Station (sometimes even the airport or Malmø) up to Helsingør (Elsinore). Sit on the right side of the train for lovely sea views here and there.
Along the line, there are a few places I’d suggest getting off.
Klampenborg – take a hike among the Elks in the UNESCO forest, visit the old amusement park Bakken, and finish with a dip in the ocean.
Skodsborg – an awesome nature playground right next to the station with covered spots for BBQs. It’s on the edge of a beautiful forest, so you might opt for a hike as well.
Humlebæk – visit one of my favorite museums, Louisiana, and walk through the forest to Krogerup Avlsgaard where you can stock up on organic produce.
Elsinore – you’ve probably already read about Hamlet’s Kronborg, but do you know about the M/S Maritime Museum? Walk the narrow alleys of the city center, visit the architecturally marvellous Kulturvæftet or jump on the ferry to Sweden. You might even decide to spend the night at the seaside hotel Marienlyst or at least visit for a half-day spa pass.
The entire stretch is only an hour’ish (not all trains stop at every station), so if you’re pressed for time, it’s possible to do a limited selection of my mentioned options and be back in the city for dinner.
Be sure to buy your ticket before getting on the train to avoid a fine.