The following places are all within an hours drive

Art

Louisiana
Statens Museum for Kunst
Arken
Rudolph Tegner
Nivaagaard
Veksoelund
Geo Art
gg Kunst
Munkeruphus

Castles / Monasteries

Castles in Denmark
Kronborg Castle
Esrom Monastery
Ledreborg Castle
Roskilde Cathedral
Roskilde Monastery

Museeums

Museum of Hunting and Forestry
The Vikingeship Museum
Nordsjælland's Toy Museum
Technical Museum
Veterantrain Museum
Zoological Museum
Hammermøllen
Folkmuseum
Holbo
Maritime-Museum
The House of Knud Rasmussen
Danish National Museum
Thorvaldsen's Museum
Karen Blixen

Sights / Amusements

Activities in North Sealand
Visit Copenhagen
Activities in Copenhagen
Hagenglas
The Garden of Berries
Falkonergaarden
Fredensborg Put and Take Troutfishing
The Sweet Life - make you own sweets
Oresund's Aquarium
Tycho Brahe Planetarium
The Viking Play
North Sealand Tropical Birds and Parrots
Zoo
Bådfarten
Frederiksdal Canoeing
Nordsjælland's Sommerpark
Tivoli
Bakken

Golf

Hornbæk Golfclub
Simon's Golf
Nivå Golf
Helsinge Golf