A beautiful Baroque convent in the Lesser Town.
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A monastery on the mountain. Worth a visit for both its picture gallery and its notable Renaissance library.
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.
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.
Katedrala svateho Vita
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.
Petřínská rozhledna'
A smaller version of the Eiffel Tower on the top of Petrin Hill overlooking Prague. The grounds near the tower contain a formal rose garden which is free to walk around. With a height of just under 60 m, it is about 1/5th scale of the Paris Eiffel tower, and was constructed shortly after its Parisian counterpart at the end of the 19th century. The tower has 2 viewing platforms, one about halfway, and one at the top. A complete ascent takes about 220 steps. Strong winds (which are common in Prague) make the tower wobble, which can be felt on the upper deck and can induce motion sickness in some visitors.
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.