Stroll around the harbor to get a sense of a real fishing town! With plenty of tasty restaurants and cute shops, you won't be bored. We especially like to get ice cream at søster's is, or kanal kiosken or to try a 'shooting star' (aka large pile of fish on bread) at Proviant.
Take a short train or bike ride to lovely Humlebæk, home to the stunning Louisiana Museum - it's an old manor house built out to house very interesting permanent and temporary exhibitions. The museum looks over the sea, and has a lovely cafe to take a cake and coffee.
Go for a walk on the lovely path that follows the coast between Gilleleje and the summerhouse village. You can start at Netto, then follow the sidewalk toward the right (west. Turnoff to the path is up two blocks on the right hand side (there are signs). The total distance is somewhere around 3km.