If on your visit you truly wish to understand this city's past and how it informs the present, this museum is an excellent place to start.
A good overview of Prague's past.
What better way to get up to speed on the history of the Golden City than to visit the Museum of the City of Prague, which offers a pretty good overview from prehistory through the present day via artifacts, paintings, graphics, pottery, furniture, and various and sundry multimedia displays. The jewel in the crown is the Langweil Model, a scale model 20 metres (66 feet) long built between 1826 and 1834 which depicts the city around the beginning of the 19th century down to an amazingly minute degree of detail. You'll find the museum at Na Poříčí 52.