There are a lot of possibilities. If you are interested in architecture, there are chruches from romanik over gothic to baroque style. There are modern architecture buildings, like the "dancing house". A nice look in the old city (or close to it) is the front of the "Jeruzalémská synagoga", which has moorish features. Ofcourse you should go up on the castle hill. There is also a change of the guard with czech soldiers.
For a nice view on the city I can recommend the "mini-Eiffel-tower" "Petřínská rozhledna" overlooking prague from a hill with a nice park. From there you can walk down to the quarter with most of the foreign embassies. There is also the german embassy close by, which is (atleast for germans) of some historical significance as part of the 1989/90 revolution/unification period. A lot of east german refugees fled to the (west) german embassy there. At some point more than 4000 refugees were on this very small compound.
I can also recommend to go to Vyšehrad, which is a star shaped fortress from the early modern era. You have a quite nice view along the moldava river.
And in the evening there is pubs with beer everywhere.