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Photo: MathKnight and Zachi Evenor, CC BY 2.5 via Wikimedia Commons
In the center of the castle and the most important cathedral in all of the Czech republic. The oldest parts of the cathedral are from the 14th century, but the cathedral was not completed in the Medieval period. The highest tower was completed in Renaissance and Baroque styles much later, as is clearly obvious. The Western portal and both Western towers are even younger, completed in the 19th and early 20th centuries. However, the original Medieval plans were used for them and their relatively small age is not obvious. St. Vitus Cathedral was the place of royal coronations and also the location of the remains of several famous Czech Kings (notably Charles IV, of Charles Bridge fame). Go around the cathedral so you not only see the Western portal with the rose window and beautiful gargoyles, but also the original medieval Golden Portal in the south and the stunning Flying Buttresses in the east. Things not to miss inside the cathedral include the stained glass Rose Window in the west portal, the stained glass window by Alfons Mucha, the tomb of St. John of Nepomuk made of pure silver, the Royal Crypt underneath the cathedral (with the graves of Charles IV, his four wives, Wenceslas IV, Ladislas the Posthumous, George of Podebrady, Rudolf II, and Marie Amalie of Austria, the daughter of Maria Theresa of Austria) and the stunning St. Wenceslas Chapel with the relics of the saint and walls decorated with gold and more than 1300 gems. The Czech Coronation Jewels are kept behind the door with the seven locks (seven important people including the Czech President and the Czech Prime Minister keep the keys) in the St. Wenceslas Chapel. If you're willing to hike the 287 stairs to the top of the Bell Tower (the one with Baroque roof) you'll be rewarded with excellent views of the castle and the surrounding area. The Bell Tower holds Zikmund, the biggest bell in the Czech Republic.
The Metropolitan Cathedral of Saints Vitus, Wenceslaus and Adalbert is a Catholic metropolitan cathedral in Prague, and the seat of the Archbishop of Prague. Until 1997, the cathedral was dedicated only to Saint Vitus, and is still commonly named only as St. Vitus Cathedral.
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Starý královský palác
The original seat of Czech rulers. Visitors first enter the Vladislav hall, the largest high-Gothic vaulted space in Central Europe. Other rooms include the Palace chapel and throne room. At the end of the exhibit is "The Story of Prague Castle" exhibit, which features artificats from the castle's past. The Old Royal Palace is occasionally closed to visitors, so it may be advisable to check this before visiting.
Pražský Hrad
The former seat of the King and is now the seat of the Czech president. This is Prague's number one tourist attraction so expect huge crowds and possibly long lines, especially during high tourist season. Your best bet is to come early, as soon as the castle opens. Similar to other royal palaces, there is an hourly changing of the guard ceremony. At noon, the ceremony includes fanfare at a flag ceremony in the first courtyard.
The second oldest church in the castle and features a colorful Baroque facade. The interior is visibly older and is the burial place of the Premyslid family and the first Czech saint, Princess Ludmila.
Schwarzenberg Palace, Sternberg Palace
The Old Masters collection of the National Gallery, covering paintings from the 15th to 18th centuries, is divided between two mansions on Hradčanské Square, the Renaissance Schwarzenberg Palace and the Baroque Sternberg Palace.
Zlatá ulička
During the reign of Rudolf II, goldsmiths lived in a lively alleyway filled with tiny workshops, which were also their residence, hence its name. Tiny, cobblestoned walkway filled with brightly-painted little houses, where modern man has a hard time standing with the low ceiling. (It's tough to realize just how tiny our pre-20th-century ancestors were until you go somewhere like this). Franz Kafka occupied No. 22 from 1916 to 1917, and this is why most people visit the Golden Lane. There is also a Renaissance tavern, a castle guard's house including his colorful uniform, and a goldsmith's shop shown as they might have looked during the periods represented, and those are interesting. Otherwise, there really isn't another good reason unless you want to buy some overpriced souvenirs in the small shops now occupying the houses.
Art museum near Prague Castle. Houses the original manuscript for Beethoven's famous 5th symphony, and many other interesting artifacts.