On the coast south of Copenhagen, the striking Arken Museum of Contemporary Art (arken.dk; adult/child 115kr/free) in Ishøj hosts large-scale contemporary exhibitions of artists such as Anish Kapoor, with a smattering of its permanent collection as well. There's a good arty shop and a nice glass-walled restaurant with a view. The museum is surrounded by a moat on a barrier island facing the sandy Ishøj Beach; a popular escape on sunny days. The beach park is worth exploring – see if you can find the hiding troll.
To get here from Copenhagen, take the S-train southwest to Ishøj station. From here, you can either catch bus 128 to the museum (five minutes), walk (2.4km), or take the light rail direct to Ishøj Strand.