Elsinore Castle, the setting of Shakespeare's Hamlet, is popular with tourists as a day trip from Copenhagen. However, one should not journey there in search of historical significance or for an inspiration for a great work of literature. Shakespeare never visited Elsinore, and if the Danish legendary figure Amleth, on whom Hamlet is based, ever existed, he lived centuries before the construction of Elsinore. The Castle, an hour's journey from the city, offers nothing to distinguish it from other European castles. It's only claim to fame is that Shakespeare happened to use it's name when he was creating what is arguably the greatest dramatic work ever produced. Your time is better spent if you instead take the shorter journey to Fredricksborg Castle in Hillerod, which is more or less a half-way point between Copenhagen and Elsinore.
Fredricksborg is by far the best of the Danish castles. It is the castle I always imagined Cinderella attended her famous ball in. Cobblestone courtyards with classical fountains are framed by the towered brick building complex with its tall pointed roofs. The picturesque bridge extends from the arched gate, over the moat, and into the charming village which centers around the castle itself. Fredricksborg isn't the biggest or most elaborate castle in Europe (although it is pretty dramatic), but I never figured Cinderella's castle was. She didn't live in Paris, London, Florence, or any other cosmopolitan city of the time, but rather in a quaint village like Hillerod, where the people gazed dreamily toward the dramatic castle that was the focal point of their town until one remarkable day, when the common women of the village were unexpectedly invited to a party there. That may only be my vision of the classic fairy tale, but Fredricksborg Castle fits it to a T.
Some of the rooms in the castle are furnished much as they were in various periods of the castle's four hundred year history, and many of the furnishings from the 17th and 18th century (as well as other periods) are authentic. Other rooms (namely the top floor) have been converted into a museum which houses the National Portrait Gallery (although many of the portraits are scattered through the other, more historically furnished areas of the castle as well). The art gallery contains portraits of Danish monarchs over the last four centuries. I suppose this is of significant importance to the Danish people, but I thought it to be the least interesting area of the palace.
To get to Fredricksborg take the A train north from central Copenhagen (during peak hours you can take the E train as well). Hillerod is the last stop. Expect about a 30 minute trip. Admission is 45 Kroner (approx. $7.50 USD).