After some calculations I decided to buy Copenhagen Day Card for 72 hours, namely three days. It will be the most economical choice, if you are planning to visit as much as castles and museum you can and traveling the places bytrain and metro. It will be unwise to not to buy this day card. You can find all relevant price information on the link above.
If you like biking Copenhagen is a perfect city to do that. You can easily find a bike rental place in the city. It is possible to rent for 6 hours to 2 months. The price of renting it for a day for per bike is around 10 euros, but you can find more expensive and also cheaper options, depends on the type of the bike.