Hellerup is the first proper suburb north of Copenhagen — upmarket coastal residential, the Strandvejen (Coast Road) lined with villas built for the bourgeoisie and the merchant class through the 19th and 20th centuries. Tuborg Havn — the former Tuborg brewery's harbour, redeveloped into offices and waterfront apartments since 2000 — is the post-industrial counterpoint to the villa-lined inland streets.
Three and a half kilometres along the coast, a hundred minutes if you stop for the harbour view. Start at Hellerup S-tog (C-line, F-line and Coast Line all stop here) — fifteen minutes from Central Station. Walk east toward the water; the villas begin within blocks.
Strandvejen is the spine. Walk north — the villas range from 19th-c Italianate to 20th-c Functionalism, set back behind gardens. The Tuborg brewery operated here from 1873 until 1996; the harbour now is offices and apartments where the lager casks used to be loaded.
End on the harbour edge with the view across the Øresund — Sweden visible on a clear day. Walk back inland to Hellerup S-tog via a different villa street if you want a second look at the architecture.