I went on an introductory tour of the city (which included coach, boat and walking tour), so I got a good sense of the four historical towns -- Staré Mêsto (Old Town), Hradĉany (Castle Town), Malá Strana (Lesser Town) and Novo Mêsto (New Town). The first time I had been to Prague (1992) I also got a sense of the Communist-era outer city, which I don't need to explore again (very ugly block buildings outside the historical centre). The building below is called The House by the Minute and is adjacent to the old town hall and astronomical clock tower in Staromêstská (Old Town Square). This beautiful building with stunning black and white sgraffito-painted facade was Franz Kafka's childhood home.
The astronomical clock -- still accurate after several hundred years -- is a thing of wonder, as well as being a major tourist attraction. Every hour, on the hour, small doors open above the main clock and there is a parade of carved wooden saints. The skeleton on the side of the clock also shifts his hour glass so you can be more aware of your mortality...
It's great to see some new architecture too! This building is called The Dancing House, which I first spotted from across the river (I was staying in the Smichov area), is an office building designed jointly by Croatian-Czech architect Vlado Miluniĉ and American Frank Gehry. It was built in 1997 with the strong support of playwright and former president, Václav Havel.
One day, after a visit to Strahov Monastery, I walked down Petřín Hill. It is a very pleasant walk down to Malá Strana, and at the foot of the park is the Memorial to the Victims of Communism sculpture by Czech sculptor Olbram Zoubek.