Frederiksberg Have is the Baroque garden Frederik IV laid out from 1697 around his summer palace on Frederiksberg's modest hill. Thirty-two hectares, formal Italian planning relaxed into English-romantic in the 19th century, with a working canal system, a Chinese Pavilion, and the slot itself — still the Royal Danish Military Academy, so visitors stay outside.
Three kilometres, ninety minutes at a strolling pace. Frederiksberg metro (M1/M2/M3 cross here) lands you at Runddel, the main gate. The central canal opens immediately west — boat trips in summer, willows year-round. Det Kinesiske Lysthus (the Chinese Pavilion) sits on a small island in the canal, J.A. Kirkerup's 1799 commission for a tea pavilion when Chinoiserie was the European fashion.
Climb the hill — modest by Copenhagen standards but the city's high point — to Frederiksberg Slot. The 1703 J.C. Ernst palace is the Italian Baroque the king imported; the working military academy is the present. View across the gardens; don't try the gates. The southern side opens onto Søndermarken, the wilder park.
Walk back to Frederiksberg metro via the canal path. Boat hire in summer is the other way to do it.