Frederiksborg Slot was once the summer residence of the royal family, and was modeled on Italian villas of the 1600s. The main building is now home to the Danish Officers Academy, so is rarely open to the public, but the surrounding grounds are one of the city's most romantic spots, and people flock here in warm weather to picnic, stroll, and enjoy open-air concerts. If you're visiting in the summertime, be sure to check the website for details on free shows. Admission to the grounds is free.