Using travel app Rejseplanen.dk, we put in journeys from the central station — which now has its own Metro stop following the opening of the new M3 line — to various landmarks in the city.

We also looked up journey times without the Metro, to see how much of a difference it has made for the trips we've picked out.

Before continuing, please note — this not a comprehensive study of the efficiency of the Metro, but rather a fun look at some hand-picked journeys to popular sights in Copenhagen.

The Round Tower

Photo: Søren Bidstrup/Ritzau Scanpix

The 17th-century tower with its distinctive cobbled walkway was originally built as an observatory, and remains a great way to see central Copenhagen from above.

City Ring: To get there, take M3 from Copenhagen Central Station two stops to the east, to Gammel Strand. From here, walk around 500 metres along Købmagergade, a busy shopping street, and you can't miss the Round Tower looming on your right. This will take a total of 16 minutes including walking within the Central Station to access the Metro, according to Rejseplanen.

Alternative: Take a suburban S-Train from the central station directly to Nørreport station, and walk from there. Nørreport is closer to the Round Tower than Gammel Strand, so this journey is actually faster at 10 minutes.

The Little Mermaid

Photo: Benoit Tessier/Reuters/Ritzau Scanpix

The diminutive but popular Edvard Eriksen statue, depicting Hans Christian Andersen's famous, Disney-adapted character, is located a short distance outside of central Copenhagen at the Langelinie harbourside area.

City Ring: The M3 comes into its own here, as it quickly brings you close(ish) to the Little Mermaid and allows you to see another, arguably more spectacular, sight, on the way. Take the underground train to the Marmorkirken (The Marble Church) Metro station. Here you can see the splendid, domed Frederik's Church, which lends its name to the new station. From here you'll have to walk 1.3 kilometres to reach the Mermaid, but most of that walk will be very pleasant, weather permitting. Total journey time: 28 minutes.

Alternative: Several minutes can be shaved off this trip by taking the S-Train to Østerport station and then bus no. 26 to the Søndre Frihavn (Kalkbrænderihavnsgade) stop. This has the advantage of getting you a lot closer to the Little Mermaid, so you save time, but miss out on the Marble Church and harbour walk. Journey: 20 minutes

Assistens Cemetery

Photo: Nikolai Linares/Ritzau Scanpix

In the heart of multicultural Nørrebro, Assistens Cemetery is the resting place of many famous Danes, including Andersen himself along with physicist Niels Bohr, pop singer Natasja Saad, philosopher Søren Kierkegaard and many others. It often doubles as a park, with Copenhageners taking a run, walk or picnic in its quiet, leafy confines.

City Ring: Take the Metro to the west, heading eight stations through Vesterbro and Frederiksberg to Nørrebros Runddel, which is at the northern end of the cemetery grounds. Rejseplanen puts this journey at 21 minutes, but it will be shorter if you don't walk around the cemetery to the main entrance.

Alternative: By taking a regional train or S-Train from Copenhagen Central to Nørreport station, then switching to bus 5C, you can get to the cemetery in as little as 17 minutes, provided connections are well-timed.

Christiania

Photo: Asger Ladefoged/Ritzau Scanpix

Anarchist enclave Christiania was founded in the 1970s when squatters took over an abandoned military barracks, and the community is still going strong. It is a draw for visitors who are keen to experience its alternative lifestyle and contrast with the more regal surroundings of Christiansborg and Amalienborg palaces across the harbour.

City Ring: This destination gives you the experience of switching from the new Metro line to the old one. Take M3 to the now-expanded Kongens Nytorv station and then switch to M1 or M2. One station down the line is Christianshavns Torv. From here, there's a 500-metre walk to Christiania. 24 minutes, according to Rejseplanen.

Alternative: Bus 9A towards Refshaleøen drops you off right outside Christiania and therefore saves you a bit of walking, cutting the journey to 17 minutes.

Tivoli

Photo: Lasse Salling, Tivoli

Perhaps the biggest tourist attraction of all in Copenhagen, Tivoli is just across the street from Copenhagen Central Station — so save your Metro, bus or S-Train fare and spend it riding a rollercoaster instead.

READ ALSO: In pictures: A look at Copenhagen's new City Ring Metro line