Would you recommend renting a car to visit Fredericksborg and Kronborg castles and the Louisiana Museum or take a train? Is there a substantial cost difference?
The train is easy, I'd choose that over a car rental. I'd suggest getting a Copenhagen card that covers all transportation and admissions. You can do both Kronborg and Louisiana as a day trip. Start early go straight to Helsingor for Kronborg (bring a flashlight or buy one from the vending machine to see the Casemates). The main castle tour is brief but good. Then stop at Louisiana on the way back to Copenhagen.
Make Fredericksborg castle a separate day trip because it uses a different train route - but still covered on a Copenhagen card ( they come in 24 hour cards but we used 72 hour cards).
Thanks for the recommendation. We will purchase the Copenhagen Card (approx 450 DKK pp for a 48-hour pass) and take the train to the castles and museum. Maybe we are biting off too much, but our plans are to start early and see Fredericksborg Castle in the morning (opens at 09:00), Kronborg Castle in the afternoon, and hit Louisiana Art Museum for dinner/evening (the museum is open until 22:00). Long day but I think we can do it. Each of the train segments is 40 minutes or less. There is some walking to the attractions from each train stop.
The next day, we will take the train to Roskilde and see the Cathedral and the Viking Ship museum. When we return to Copenhagen later that day, we hope to take a canal tour and see Tivoli Gardens at night. The Copenhagen Card is good for all of these attractions including train transportation -- it's a really good deal.
Train is best way for most day trips from Copenhagen. Look for short cut through woods to Louisiana, great place for lunch on the sea.