Photo: Matěj Baťha, CC BY-SA 2.0 via Wikimedia Commons
A monastery on the mountain. Worth a visit for both its picture gallery and its notable Renaissance library.
Strahov Monastery is a Premonstratensian abbey founded in 1143 by Jindřich Zdík, Bishop John of Prague, and Vladislaus II, Duke of Bohemia. It is located in Strahov, Prague, Czech Republic.
© OpenStreetMap contributors
A beautiful Baroque convent in the Lesser Town.
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.
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.
Due to a housing crunch, most young Czechs don't move out of their parents' house until they marry (sometimes long after!) This lack of privacy leads to some very public displays of affection – what you see on the metro or trams won't compare to what you’re likely to encounter on Petřín Hill. This hillside slopes down from the Castle and Strahov Monastery to Malá Strana and Malostranské náměstí metro station. It affords an amazing view of the city on a clear day, and in springtime the trees are all in bloom. This is possibly the nicest place to kick back with a bottle of wine and your significant other to watch the sun set over the city. Just be careful not to trip over the modesty-lacking couples who will probably already be there. In a city filled with apartment buildings and only a handful of single family houses (almost all in the diplomats' favoured housing area, Dejvice, and priced far above the average Czech family's wage) parks take on a greater importance. The most famous "inhabitant" of the park is a statue of poet Karel Hynek Mácha, at whose feet lovers leave wreaths every spring in honour of his romantic poem Máj.
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.