When in Prague, visit the Muzeum hlavního města Prahy. It is only one of the many museums in Prague but it is so informative of the history of the city.
One amazing permanent exhibitions is the “Langweil’s Model of Prague”. It is made of paper and was made by Antonin Langweil between the years 1826 - 1837.
It shows that the city hasn’t changed much and you will be able to identify many places.
The museum is easily got to from Metro Line B or C, Florenc station.
That is a great tip! Just for your information Muzeum hlavního města Prahy means Museum of the capital city Prague. So this museum is about Prague.
You are right that the city center did not change much over the time. It is partly because Prague was not much destroyed during World Wars and also because the whole city center is on the UNESCO list and in order to stay there it has to maintain its historical look