Prague Castle, St. Vitus's Cathedral, Basilica of St. George

Several of the best things to see in Prague are in the Castle. I suggest going early, there are lots of people, even on a cold November day. If you need food, find someplace well away from the castle to eat, prices get ridiculous in that part of town. I also suggest going through the front section on the western face, and not through the back section, even though the eastern steps are closer to the river. A great spectacle is the changing of the guards at noon. A mini-version that happens on the hour, but this one is worth seeing.
Arrive early under the gruesome gate to get a spot in the courtyard. The guards are awesome to watch, but Americans and Brits will definitely notice a difference between the Czechs and their own Marines. Pant cuffs may bag a little at the ankle, there's some shuffling in ranks to evenly space the men, some movements aren't all that snappy, and it's obvious not everyone takes 'coming to attention' as seriously as others. Simply, the Czechs take their duty seriously, but they don't make it the religiously martial ritual that their Anglo brethren do.

They do however, have a really jazzy bunch of brass to do it to though. And they are a very engaging spectacle. Well worth the watch. I am reminded that at some point I must acquire a sword. For the inside I recommend buying a “Maly” ticket for 250 kc which grants you access to the Old Royal Palace, the Basilica of St. George, and the Golden Lane. The Cathedral is free entry. Order of operations should be something like this: get there at 11:30 to go in and buy ticket, go find spot for changing of the guard. Once done, bypass the Cathedral (everyone is going there), the Palace would be a good option. Then the Cathedral, the Basilica, and the Golden Lane, with a leisurely stroll down the stairs towards the river. This is enough to occupy you for three or four hours if you're a thorough tourist.

The Palace was looted by the Nazis and is fairly small. Don't go in expecting much. I enjoy the idea of a modest monarchy, though. However, it does contain what I'm told is the largest Gothic vaulted space in Europe (or the world, I suppose), and the stonework is quite beautiful. Go upstairs to see the old coal fired ceramic heaters and some documents about failed rebellions. At the far end of the Hall is a small throne room and a church.

St. Vitus's Cathedral is pretty impressive.
It was 800 years in the making has beautiful stained glass windows, one of them by Alfons Mucha. I'm not really into the religious stuff, but I dig cathedrals for the architecture and art. Vitus's is pretty cool on both counts.

Halfway down on the right side there is a tower that you can climb. It's something like 287 steps up a spiral staircase. This isn't terrible until you must share this staircase with the people coming down, as well, and you get squeezed to the inside where the steps are only four inches deep. Can be a bit aggravating. The top will be crowded, but it was far and a way the best view of Prague I had the whole time I was there.

The outside of St. George's Basilica is a lovely red and white, reminding me of an Orthodox church. The inside is very primitive and was severely neglected under Communism, but it still holds a certain majesty. I was quite impressed with the frescoes on the ceiling in the front.

I wasn't too impressed with the Golden Lane. It's a bunch of little cottages built up against/into the outer wall. Once the artisans lived there, especially the gold workers for the monarchy/cathedral (hence the name), and Kafka is supposed to have lived there for a short time. Now it's chockablock with tourist kitsch and the tourists themselves. I'm told I missed the actual historical display part: go left when you get through the gate? Also: don't buy any food here unless you're will to pay true tourist prices. Prague is usually double what things cost in Brno, hot wine or simple food in the Castle is triple.