Dyrehaven is the royal deer park — eleven hundred hectares of UNESCO-listed forest north of Copenhagen, founded by Frederik III in the 1670s as a royal hunting reserve and still home to around two thousand deer. Eremitageslottet — Lauritz de Thurah's 1736 hunting lodge — sits at the centre on a small ridge, where the royal hunting parties used to dine. Bakken — the world's oldest still-operating amusement park, dating to 1583 — is at the park's southern gate, doing the cheerful-noisy counterpoint.
Five kilometres on the forest paths, two and a half hours including stops. Klampenborg station is the entry point — the Coast Line drops you a minute from the Røde Port (Red Gate). Bakken is right there on the southern edge; pass through if it's open (March–August), but the deer-watching is the main event.
Walk north on the central allée — the trees thin out at the rises, and the deer (red, fallow, and sika) graze in the open meadows between the wooded stretches. Eremitageslottet is the centrepiece at the top of the ridge; closed to the public most days, the building itself is the experience from outside.
Back south to Klampenborg via the deer-watching path. The Coast Line takes you back to Copenhagen in twenty-five minutes.