1. The Little Mermaid: Visit the iconic statue inspired by Hans Christian Andersen's fairy tale, located on the Copenhagen waterfront.

2. Nyhavn: Stroll along the picturesque canal lined with colorful buildings and enjoy the lively atmosphere of restaurants, cafes, and street performers.

3. Amalienborg Palace: Witness the changing of the guard at the official residence of the Danish royal family. You can also explore the palace grounds and gardens.

4. Christiansborg Palace: Explore the seat of the Danish Parliament and the official site of the Prime Minister's Office. Entrance to the palace is free, and you can visit the ruins of Bishop Absalon's Castle under the palace.

5. The Round Tower: Climb this 17th-century tower for panoramic views of the city. The tower also houses a unique art gallery and an astronomical observatory.

6. Botanical Gardens: Wander through the beautiful green oasis, home to an extensive collection of plants from around the world. The gardens are perfect for a leisurely walk or a picnic.

7. National Museum of Denmark: Discover the rich Danish history and culture through the museum's exhibits, which include Viking artifacts, medieval art, and ancient Egyptian mummies.

8. Assistens Cemetery: Pay a visit to the final resting place of famous Danes such as Hans Christian Andersen and Søren Kierkegaard. The cemetery is also a tranquil park, ideal for relaxation.

9. Tivoli Gardens: Although entry to Tivoli Gardens is not free, you can enjoy the vibrant atmosphere and catch a glimpse of the exciting rides and beautiful gardens by strolling through the adjacent City Hall Square.

10. Superkilen Park: Immerse yourself in the diverse cultures of Copenhagen as you explore this urban park, known for its unique design and international influences.

Remember to check the opening hours and any special guidelines before visiting these attractions. Enjoy your time in Copenhagen!