We go often--we have faves and a special walk we enjoy, too. It's tram to funicular, to hilltop (w/stop at House Nebozizek halfway) onward to obseravtion tower (lift never works in the 5 yrs we've been going) have a wurst,hit the restrooms, walk on to Strahov Monastery(if you like art museums, there is one on the way) Wander around to the castle distrcit--find the garrison where soldiers comeout and follow them to the chaning of the guard--skip the $$ admission to castle--head straight to St. Vitus cathedral(free) and stand in awe of the most exquisite stained glass work from Alfonse Mucha--wander around the caastle gardens and work you way down the steps to the tram stop---or cross over to Thunovska street or Nerudova and have a few BEERS at a courtyard cafe.
Got lots more info--when are you going?? I think we're arriving 27 sept.