Here is a special post on public transport in Prague for those who need to get from the airport to the city or just want to move around the city .

A nice way to start a tour here might be one of the two observation towers (there are more but only two are high enough to oversee the whole city).
My favorite is the old one at Petřín, built in 1891 as an approximate imitation of Eiffel Tower in Paris. You can get there several ways; the most popular one is from the street Újezd (there is a tram station of the same name, close to a nice park that stretches up the whole way to the top of the Petřín hill). It is a nice walk but those who do not like walking up the hill, there is a cable railway. In the tourist season, there may be a long line of people waiting for the ride.

To get to the top of the tower, you can climb up the staircase, or you can use an elevator. There are two platforms; the lower one is too low to overview the city but it is less crowded. From the top platform, the view is fantastic. Here are some pictures.

 1-The Prague Castle (Pražský Hrad); 2-Saint Vitus Cathedral (Chrám Svatého Víta); 3-Schwarzenberg Palace; 4-Hradcany Square (Hradčanské náměstí) with all the beautiful palaces next to Prague Castle); 5-Italian Hospital (Vlašský špitál; currently a part of Italian Embassy); 6-Hotel Internacional (the communist era relict, built in Socialist Realism style, resembling the Moscow’s Lomonosov University); 7-Troja Chateau (Trojský zámek, a very nice castle next to the famous Prague ZOO)

8-St. Nicholas Church (Chrám Sv. Mikuláše, impressive Baroque church); 9-AC Sparta Praha Football Arena (home stadium of one of the top Czech soccer teams)

10-Charles Bridge (Karlův most, the famous 14th century stone bridge with towers on both sides, both accessible); 11-B.Smetana Museum (Muzeum Bedřicha Smetany, the Czech national composer); the Old Town Bridge Tower at this side of Charles Bridge leads to the Knights of the Cross Square (Křížovnické náměstí), a very small but one of the most beautiful places in Prague; 12-Rudolfinum (the home scene of Czech Philharmonic); 13-Church of Our Lady before Týn (Týnský chrám, beautiful 14th century Gothic church with two towers, better visible from here than from the Old Town Square where it is hidden behind the square houses; the single tower close by is the Old Town Hall with the famous astronomical clock); 14-Prague main railway station (Praha hlavní nádraží)

15-Žižkov TV Tower (Žižkovský vysílač, the other great observation tower, at 216 meters the highest building in Prague); 16-National Museum (Národní muzeum, this is the historical building at the upper end of the Wenceslas Square-there are other buildings, e.g. a new one right across the street, but this is the original and the main one); 17-National Theatre (Národní divadlo)

18-Church of St. Ludmila (Kostel sv. Ludmily, neo-gothic roman catholic church at Náměstí Míru); 19-Dancing House (Tančící dům, the most famous modern building in Prague, built in 1996 by Frank Gehry and Vlado Milunić); 20-The Church of Virgin Mary at Slovany (Kostel Panny Marie na Slovanech; a part of the gothic monastery also called Emauzy; the church was bombed in World War II and though the main body has been preserved in its gothic style, the shape of the  tower is modern); 21 Nusle Bridge (Nuselský most, the highest bridge in Prague is not over the Vltava River but over the valley called Nusle; the high building at the end of it is a hotel called  Corinthia Towers; there are ruins of the original castle of Prague called Vyšehrad close by, just out of the picture-hopefully next time I take it all…)