Well, RJ that calls for a long answer. Let me just put down some ideas, I am not sure what your passion is.
- there is a church downtown, one of the bests organs in Europe and every Sunday 10AM there is a free concert.
Here is more
- Kutna Hora is a town near Prague,
huge church It was silver mining town and St.Barbora is the saint for miners.
- Moravia is the east end of CR - you can go there to see wine cellars and have merry good time.
- Castles are everywhere, like
Karlstejn,
Konopiste Konopiste is full of game trophies - thanks to Ferdinand d'Este and you could play golf on the hill cross the river from Karlstejn
- you could take a boat ride on the river in Prague, definitely way to ssee the city
- Prague zoo is truly amazing - but you dont go that far to see animals
- to see the city from different angle - Vitkov is great, also the TV tower in Zizkov, or get up to the piedestal of former Stalin's statue
- you can follow the river bank from Vyton - Prague 4 to Karlin and see a lot and eat local food and drink Czech beer
- Plzen (Pilsen) is town west from Prague - pilsener originated there
- Ceske Budejovice is south of Prague, the original Budweiser is brewed there
- Karlovy Vary is bath town west of Prague, beautiful too
- Prague 2 Vinohrady you can find some nice and not so nice but authentic pubs with beer and local food - worth exploring too
+ there are the typical turist places like Brewery U Fleku, Charles Bridge, Castle, St Nicolas. If you are up to it, you can climb the tower of St. Nicolas, the communist police had a listening post there and it is an amazing vew
I could go on and on, there are hikes to take in mountains or follow river near Prague but I am not sure what your preferences are.