Your trip to Copenhagen should not be that pricey. For a number of tourists, watching the city is enough for them to make their trip worthwhile but that is nearly impossible for others who wish to get to know the city very well. There are a lot of free attractions available in the land of smiles and others even are very affordable. Just because the city is located in one of the most expensive countries in the world does not mean everything is very expensive.
The National Gallery of Denmark provides free admission to the permanent exhibitions of the museum while selected special ones like The Round Tower and Danish Architecture Center has a cheap admission fee. You can also go on sightseeing while riding on a boat and experience the greatness and beauty of the place. If you came in at the right time where the weather is right, you can make your own food and bring it with you on a picnic without having to spend a dime in a restaurant. You can pick up food from one of the supermarkets of the city and find a good place in one of the parks and gardens in Copenhagen such as Frederiksberg Gardens or King's Garden. Other gardens include Amaliehaven, Botanical Garden, The Deer Park, The Rampart of Christianshavn, The Rose Garden, Fælledparken, Kalvebod Fælled Vestamager, and the Ryvangen Memorial Park.
Do not forget to bring along or get your own Copenhagen Card in which it entitles you to free admission through 75 different attractions and museums, free public transport by Metro, train and bus and discounts from a number of sights and restaurants. You can bring your 2 kids along with you and you are lucky if both are below the age of 10 as they are free from fare charge in public transport.
Free guided tours are provided that lasts for three hours which takes place every summer season at the City Hall starting eleven in the morning. The tours will give you an insight about Copenhagen which will make you learn about the Marble Church, Nazi Occupation, WWII Resistance, Danish Royal Palace, Tivoli, the oldest royal family in the world and many more. Another free admission is the Open Air Museum located at the north of the city is one of the oldest and largest open air museum in the world. You will also find two of the oldest amusement park of the world just north of the city.