Copenhagen

Christiansborg Tower

This is the sleeper move: ride the lift 106 m up the tallest tower in the city for a full 360° over the rooftops, harbor and spires — and it costs nothing. Go early, right at opening, before the line at the King's Gate builds and before the platform fills (space up top is tight).

When you come down, walk two minutes to the Royal Library Garden behind the palace — a hidden, hedged courtyard with a fountain and Kierkegaard's grave-quiet calm. A perfect free pairing.

Rosenborg Castle & King's Garden

A storybook Renaissance castle holding the Danish crown jewels, set inside Kongens Have (the King's Garden) — Copenhagen's oldest royal park. The castle has a timed-entry ticket and sells out in peak summer, so book a slot ahead; the garden around it is free to wander any time.

Bring a coffee and sit on the lawns out front — half the city does in summer. The garden alone is a lovely, no-cost stop even if you skip the interior.

Amalienborg Palace

The royal family's winter home — four rococo mansions around an octagonal square. The changing of the guard happens daily at noon (the guard marches over from Rosenborg around 11:30), but honestly it's not that interesting: drop in if you're passing, don't build a day around it.

The square and the view down to the Opera House are worth the photo regardless. Pop into the museum only if rococo interiors are your thing.

Marble Church (Marmorkirken / Frederik's Church)

Right across the square from Amalienborg: a domed rococo church whose ~31 m cupola is the largest church dome in Scandinavia. It anchors one of the city's great sightlines — the axis runs from the Opera House, across the harbor and through Amalienborg's square, straight to the church's front steps. Free to step inside and look up at the painted dome.

The real move is the dome tower climb — a guided walk up between the inner and outer domes to a balcony ringing the cupola, with a sweep over the rooftops and, on a clear day, all the way across the Øresund to Sweden. Access is by guided tour only and times are limited, so check tower tour times before you go.

The Round Tower (Rundetaarn)

A 17th-century observatory you climb via a spiraling cobbled ramp — no stairs — to a rooftop platform over the old town. Quick, cheap, and a nice second rooftop angle to pair with (or substitute for) the Christiansborg Tower.

Copenhagen City Hall (Københavns Rådhus)

The 1905 National Romantic city hall on Rådhuspladsen — free to step into the building during office hours, where Jens Olsen's astronomical World Clock ticks in the entrance. Two extra-cost add-ons: a guided tour of the grand interior, and a separate climb up the ~106 m tower (one of the city's tallest, ~300 steps, no lift) for rooftop views over Tivoli.

Kronborg Castle

The "Hamlet" castle out at Helsingør, a UNESCO site guarding the narrow Øresund strait. It's a real day-trip — about 45 min by train each way — so commit to it as its own half-day rather than squeezing it between city stops.

The casemates (dark dungeon tunnels under the castle) and the ramparts with their cannon-line over the water to Sweden are the highlights.

Torvehallerne

The reliable lunch hit: two glass-roofed halls at Israels Plads with 60-plus vendors — smørrebrød, fresh fish, cheese, coffee, porridge, tacos. Graze a few stalls rather than committing to one. Right by Nørreport station, so easy to fold into any day.

Reffen

Copenhagen's big open-air street-food yard out on Refshaleøen, right on the water with shipping-container kitchens, a bar scene and harbor views. Sustainability-minded vendors, lots of variety. Take the harbor bus or bus 9A — it's a bit out, so make an evening of it.

Broens Gadekøkken

The street-food spot to hit near Nyhavn — sit on the water at the foot of the Inner Harbour Bridge, between Nyhavn and Christianshavn, with knockout views back at the colored houses. This is the eating answer to Nyhavn (see below): walk over the bridge and eat here instead of paying tourist prices on the quay.

Nyhavn

The postcard: a row of gabled 17th-century townhouses in candy colors lining an old canal full of wooden boats. Absolutely worth the visit and the photo — but don't eat here. The quayside restaurants are pricey and middling. Soak it in, then walk to Broens for actual food.

It's also the launch point for the canal tour below, so you'll likely pass through anyway.

20 Grams Coffee

The coffee stop on your list — a specialty café at Kampmannsgade 1, next to Vesterport station and an easy walk from Tivoli and Rådhuspladsen. A roomy, museum-ish space with good brews and pastries; handy to slot between stops in the city center.

Tivoli Gardens

Worth it — and best in the evening, when the gardens light up and there's often live music or fireworks. The 1843 amusement park is part funfair, part lush garden, part Copenhagen institution; you can wander on a park ticket and skip the rides if you just want the atmosphere.

Botanical Garden

A leafy university garden with lakes, rockeries and the gorgeous Victorian Palm House. The garden itself is free; only the Palm House and the summer Butterfly House charge admission (and those want a booked time slot). Easy to pair with Rosenborg and SMK — they're all in the same museum cluster.

SMK — National Gallery of Denmark

Denmark's largest art museum: seven centuries of Danish and European work, from old masters to a strong modern wing, in a grand building backing onto the park lakes. The permanent collection is free; only special exhibitions are ticketed. Worth an hour or three depending on your appetite.

Glyptoteket

An idiosyncratic gem behind Tivoli: Carl Jacobsen's collection of ancient Mediterranean sculpture and French/Danish painting, wrapped around a glass-domed Winter Garden of palms and a fountain. The indoor garden alone is worth the stop — a calm, warm retreat on a gray day.

Assistens Cemetery

Not morbid — a beloved green park in Nørrebro that locals picnic and stroll in, where Hans Christian Andersen and Kierkegaard happen to be buried. Free to wander; tree-lined paths and a quiet, leafy break from sightseeing.

Superkilen

A wild, ribbon-shaped public park in Nørrebro designed as a collage of street furniture from 60+ countries — Moroccan fountains, Japanese cherry trees, a black-and-white-striped plaza. Free, photogenic, and quick; an easy add-on near Assistens.

Christiania

The free, self-governing neighborhood in Christianshavn — a 1971 squat turned green, low-key commune of workshops, murals, music and homemade architecture. Free to enter and worth an unhurried afternoon. Treat it as someone's home: walk slowly, ask before photographing, and respect the no-photo zones. (Note: buying cannabis is illegal everywhere in Denmark, Christiania included.)

Cirkelbroen

Olafur Eliasson's "circle bridge" in Christianshavn — five round platforms with ship-mast poles that nudge you to slow down as you cross. A small, cool detour rather than a destination; works nicely on the walk between Christiania and the harbor.

Kastellet

A remarkably intact 17th-century star fort with grassy ramparts, a windmill and a moat — a peaceful loop for a walk, right next to the Little Mermaid statue (which you can knock out in the same stroll). Free to wander the grounds.

Swim in the harbor (Harbour Baths)

The water's clean enough to swim in — that's the whole flex of this city. The original and best-known harbor bath is at Islands Brygge, with lap pools and kids' pools right in the harbor and a sunbathing deck. Free; bring a towel and go on a warm afternoon.

Canal tour

The best cheap way to see the city's good side — an hour on the water past Christiansborg, the Opera House and the Little Mermaid, gliding under low bridges. Prebook; the popular Nyhavn departures fill up in summer. Stromma's classic tour leaves right from Nyhavn.

Royal Library — the Black Diamond

The waterfront extension of the Royal Danish Library — a sheer black-granite cube cut at sharp angles, with an atrium that opens onto the harbor. Free to walk in: ride the escalators, catch the painted ceiling, grab a window seat over the water. A quick, striking architecture stop near Christiansborg.