To get around Copenhagen, consider renting a bike or using public transportation, such as the metro or buses. A 24-hour bike rental is around 12 USD, while a 24-hour public transportation pass is around 15 USD. If you plan on taking a day trip to Helsingør, you can take a train from Copenhagen Central Station for around 20 USD round trip.
If you want a more relaxed trip, consider adding an extra day to your itinerary. With three days, you can take more time to explore Copenhagen's many parks and museums. If you're short on time, consider skipping the day trip to Kronborg Castle and spending an extra day in Copenhagen instead.