In Fredensborg, don't miss a visit to the palace gardens; if you walk around the outer track of the park, the trip is 4.5 km long. Make sure to stop at Sørup, where there's a lively environment with an ice cream kiosk, café, Restaurant Skipperhuset, and boat trips.
Fredensborg town is cosy with a slightly different selection of shops. You can rent a bike and explore the area with one of these beautiful cycling route suggestions. Also, remember that a lot is happening along the Øresund coast. Here you'll find the Louisiana Museum of Modern Art, the Nivaagaards Collection, and several charming and active harbours.