Prague Castle
Prague Castle is one of the must-sees in Prague. It's like a little village, with palaces, cathedrals, and houses inside of the walls. The best way to visit it is to take the 22 tram past the castle stop to Pohořelec stop. There's the Strahov Monastery there, and then follow the tour groups as I did past the monastery and towards the castle along this road with amazing views of Prague. I learned about this approach to the castle thanks to the Prague edition of "In Your Pocket" (the free guide which you can find in some hotels, otherwise download).
At some point you'll have to climb back up to the main road that takes you to the castle entrance.
My favorite building was the Old Royal Palace. I've never seen such an open and delicate structure, composed of these graceful intersecting arcs.
The hardware detailing is also great. I liked this guy in the door handle.
A big treat for me was to catch the changing of the guards just in time. The main event is at noon, and you want to stand in the first courtyard just behind the rope that the guards set up just before the event. The guards are quite friendly - here they are posing with some girls. There was quite a line of girls who wanted to pose with them, and I believe they obliged anyone who wanted to get their picture taken.
The changing of the guards ceremony itself was quite nice to see, but even better to hear. You can see the musicians playing their instruments through the windows of the first floor (above the ground floor) on the right. I loved the music. It was jaunty, as you would expect militaristic music to be, but there was also dramatic tension in it, like it was accompanying a Broadway musical. You can hear some of this music in the first part of this video I took. Yes, I had a really good view of the ceremony!