One day is not too much for visiting Prague, but you can make a very nice route with main highlights anyway.
The route starts at Pohorelec, Prague 1. You can reach this point by tram 22 or with taxi (please read here). It is about 800 metres from Pohorelec to Prague Castle. On the left side you will see the Palace Cernin (Ministry of Foreig Affairs) and Prague Loreto.
Prague Castle has three courts. On the third court there are the most important monuments: St. Vitus Cathedral, St. George Basilica and Old Royal Palace. From the third court you can continue to Golden Lane.
From the Prague Castle there are Old Castle Steps which lead to Lesser Town (Mala Strana) . It is about 600 metres to the Charles Bridge. After crossing the river Moldau you will reach the Old Town. Enter to the Karlova street (on the left there is Clementinum palace) which will bring you to the Old Town Square. Here the route ends. You can visit the big tower of the Old Town Hall and enjoy the beautiful Prague panorama. And do not forget to see the Astronomical Clock with 12 Apostles.
Having just two days for seeing Prague is not optimal, but it is still better then having just one day... For the fist day of your visit - please see the "Prague in one day", for the day two we recommend this following route.
The first half of this route focuses on Jewish monuments and starts on the Old Town Square. If you have not visited recommended highlights of this square previous day, you can do it now. The route continues to the street Parizska. You can see Baroque church of S. Nicholas on your left. Parizska street will take you to the Jewish Quarter. In the end of the street, on your left, you will reach the most important synagogue - Old New Synagogue. Turn left and go to the street "U stareho hrbitova" where you will find the information center, where you can buy tickets for all Jewish monuments.
After seeing the Jewish Quarter go back to the Old Town Square. Turn left to the Celetna street and go to its end. You will see the pseudo-Gothic tower "Prasna brana" which stands next to the beautiful Municipal House. From here ("nam. Republiky") continue to the street "Na Prikopech" which will take you to the Wenceslas Square. Going toward its peak you will reach the St. Wenceslas statue and National Museum.
Three days for seeing Prague is optimal. Please, see "Prague in one day" and "Prague in two days" and here is the route for the third day of your stay in Prague.
Third route starts in Belvedere at Castle district. You can reach this point by tram 22 or with taxi (please read here). From Belvedere continue to the 2nd and 1st court of the Prague Castle. Leave the Castle and go down by the street Ke Hradu and Nerudova. You will reach the Baroque church of St. Nicholas.
Enter the Karmelitska street and after 300 metres you will have church of Our Lady Victorious on your right - a place where you will find the Infant Jesus of Prague. Go back through Karmelitska street to the Malostranske namesti and continue to the Letenska street. You will have Valdstejn Palace on your left with the entrance to the beautiful Valdstejn Garden.
In four days you can see all the most important monuments in Prague. For the first three days please read the previous routes, here is the route for the fourth day.
This route of New Town starts in the peak of Wenceslas Square, under the National Museum. Go down the square and turn left at its bottom. Enter to the Narodni street and go till its end. There is National Theatre on your left, on your right you will see a beautiful view towards the Prague Castle.
Turn left and go along the river through Masarykovo nabrezi. There is Palace Zofin on your right (on the Zofin island). After 500 metres you will reach Dancing House. Turn left to the Ječna street and after 200 metres you will have Ss. Cyril and Methodius Cathedral on your left.
Go toward the Charles Square and you will stay in front of St. Ignatius Church on the Charles Square. The route can continue to the Vodickova street, which will take you back to the Wenceslas Square.