Both Staromestske Namesti and Vaclavske Namesti (The Old Town Square and Wenceslas Square respectively) have been the sites of many historical events in the city. The former was Prague’s main market place between the 10th and 20th centuries, in which there have been numerous executions, and the latter has seen many protests and the proclamation of the end of communism in Czechoslovakia.
Today, Wenceslas Square is also renowned for the shopping opportunities that it offers. I have to say that I didn't spend very much time here as I found it a little disappointing. It is not a traditional square so much as a very wide, long street and although there are some lovely shops here they tend to be rather expensive and interspersed with the usual big brand name high street shops you might find at home. At one end there are a number of stalls selling artwork, various crafts, and other wares aimed mainly at tourists, many of which are very nice and quite reasonably priced.
In contrast, the Old Town Square has a much more relaxed atmosphere. With beautiful buildings of many different styles, churches, outdoor restaurants, and often live bands playing, it is a wonderful place to spend a couple of hours relaxing after a hard day of sightseeing. Here, like in Wenceslas Square, you will find more stalls selling souvenirs and crafts. This is probably my favourite part of the city and my friends and I tended to use this square as a starting point from which to explore other areas and the surrounding streets as there is a metro station very nearby (Staromestska).
For a great view across the city, go up to the top of Staromestska radnice (the Old Town Hall). This will cost about 30kc (65p/$1). The views of the square itself, the streets adjoining it and the city’s rooftops are fantastic and completely different to those you get from other high points. On a practical note, there are toilets in the Old Town Hall before you reach the ticket desk and the price to use them is cheaper than that charged by restaurants and the museum on the other side of the square. Outside the Old Town Hall you will find the striking 15th century astronomical clock. On the hour, you can see the 12 apostles parade past the small windows at the top of the clock. As the time for this approaches, very large crowds of tourists gather to catch a glimpse. To be honest you can't really see all that much and it's nothing special. The clock can definitely be better appreciated at more quiet times of the day (or hour!) when you don't have to fight your way through the masses to see it.
There are more restaurants and nice shops on the walk from the square to Charles Bridge, via Karlova. During the day the bridge is usually heaving with tourists and it's much more pleasant in the evening, when you will often find live music being played and you can see the castle and cathedral glowing in the darkness on the other side of the Vltava.