Prague is a great place just to wander about - I'd take a walk along the old royal route.
Start at the Old Town Square - where you can see the Astronomical Clock and Tyn Church - then do along Husova to the Charles Bridge - cross over, taking in the views of the castle and the the statues lining the bridge, then walk through Mala Strana - possibly dipping into the St. Nicholas Church with its amazing baroque interior - before climbing up Nerudova and cutting accross to look around the castle and St. Vitus Cathedral.
Then wander up towards the Loreto and reward yourswelf with a large glass of dark Velkopopovicky Kozel beer at Hostinec U Cerneho vola (Loretanske namesti 1, Hradcany) my favourite beer hall in Prague. They also do a fantatic snack of scrambled egg and onion with bread or some sausage and mustard.
Just wander about, get lost in the side streets and explore that way. As for bars there are loads of great places - I'd also recommend Pivince Radegast - loud. popular, smoky, bit spit and sawdust but all the better for it - can't find the address off hand but it's near-ish to the Old Town Square through an archway off Celetna. There is a great little place popular with locals on Ovocny Trh, just up from the Estates Theatre - can't remember the name but if your back is to the theatre it's on the left hand side towards the other end of the street! Pub II, 15 Na Kampe, Kampa Island
is also a great place to have a drink and Kampa Island is a lovely place to wander about. The Konvikt Pub at Bartolomejska 11 also sells a good glass of Gambrinus.
Enjoy Prague, you'll have a great time!