What is called Prague Castle (or Pražský hrad) is actually a huge complex containing museums, churches, palaces, and gardens. The immense Gothic cathedral of St. Vitus is dominant on the skyline. The Castle complex, high on its hill above Charles Bridge and the Vltava River, is the focal point of Prague.
You can just go to wander - it's free to enter the Castle, even at night - or you can pay to enter some of the buildings and get a more in-depth view. Either way, the grandeur of the place will keep you busy for at least half a day. After all, this is the biggest castle complex in the world.
The buildings range from the Romanesque to the Gothic. The Royal Palace itself was home to Bohemian kings during the 9th century. The Basilica of St. George dates from the 10th century. You can also visit the Riding School, the gardens (open in the summer only), and Golden Lane, a charming row of medieval houses from the old goldsmith's district.
The Castle complex rides atop the hill over central Prague - you can't miss it. It's quite a hike up there, so you may want to get a tram. Get off at stop 22 (Pražský hrad) and turn left.
