The itinerary for each city varies depending on a travellers personal preference - whether they want to spend the day on a beach or in an art gallery, shopping in the designer district or the flea markets.
A quick getaway in this capital city would entail seeing these tourist attractions in my opinion and the best way to see them is to cycle around Copenhagen. Copenhagen is called the city of cyclists and rightly so - they have separate routes for people cycling on all their roads and even in the freezing cold one can see cyclists all over the city. If you aren't too keen on that then you can take a hop on/hop off bus tour like we did and they cover all these spots.
The Famous Tivoli Gardens - We were in the city for New Years so the Tivoli Gardens was a major attraction. It was elaborately lit up and had the best fireworks display at 11 pm on the 31st December. The entrance is $16.5 (Rs. 1100) on weekdays and $17 (Rs. 1200) on weekends. Everything that you do inside has to be paid for separately.
The Tivoli Gardens have been around for almost 150 years. It has everything that one needs for a day out from eateries to cafes to theatres and of course rides. This is what gave inspiration for the world famous Disney World all over the world.
Nyhavn - This is a beautiful postcard perfect 17th century waterfront canal in Copenhagen. It is the perfect place to go for a night out or to spend a beautiful summer day with many pubs and dining options. The buildings are symmetrical and consists of 17th and 18th century townhouses in different colours which is a wonderful sight.
At one end it has the memorial anchor commemorating 1700 Danish officers and sailors who lost their lives during World War 2.
The canal boat tour for the Red Bus also begins from Nyhavn.
Amalienborg Palace - This is for anyone interested in royal history or politics actually since the Royal Family of Denmark still resides inside this palace. Everyday at 12.00 one can see the changing of the guards here. The Marble Church is a 2 minutes walk from here and is another tourist spot in this area.
The Rosenborg Castle - This is a renaissance castle and was originally built as a summer house for the ruling king in the 17th century. The gardens also known as the King's Gardens is the country's oldest royal garden.
Across the castle are the Botanical Gardens which cover an area of 10 hectares and consists of glasshouses dating from 1874. The entry is free and it is open to public barring special exhibitions.
The Little Mermaid - This is a small (4.1 ft) and unimposing statue of a Mermaid and has been a symbol of Denmark since 1913. It has become the iconic statue of Copenhagen like the Merlion in Singapore or the Taj Mahal in India.
It has been vandalised several times in the past decades but has been restored time and again.
The city has several art galleries and museums depicting its history and culture. If one sets out to explore all of them in detail, it could go on for atleast a week. But for someone going there for a short break these would be the top five popular spots. The canal cruise is wonderful in the summers as well.