Walk the city for hours -...
Walk the city for hours - everywhere you turn, you will see amazing architecture and historical sites! Visiting the local galleries - the owners are very friendly and very proud of the Czech artists (as they should be). They will give you more information on the city than any tour!
Food to try in Prague: Trdelnik
Called Trdelnik, or Trdlo, this fire roasted doughy treat is made by wrapping a strip of dough around a long pole and rotating it over a fire. once it is golden brown, they finish it with some cinammon sugar and there you go! It is tasty stuff! You can find stands around Old Town selling this...it is available everywhere during holiday seasons like Easter and Christmas. Try it out!
WWII in the city
I have been to Prague during 60-years anniversary of the end of the WWII. There were many celebrations in the different parts of the world. In Prague it was adaptation for city scene of the story of last days of the war when the city was freed. You see I could steal up to Fascist's vehicle and made a photo for Czech Army :-).
Soviet Warplanes and Czech Gliders
If you like aviation and have time in Prague to take a bit of a daytrip, visit the Letecke airforce museum. Some wonderful examples of Soviet Military Aviation at its giddy cold war heights. (http://www.luftfahrtmuseum.com/htmi/imh/czm.htm)
Afterwards, go take a glider flight at Aeroklub Letnany http://www.monolit.cz/lklt?nobody&form=2064609.0&item=2162693.0&lang=642
They fly over old soviet airbases and will let you take the controls if you ask politely enough. Definitely worth the trip!
OK, so the castle...
OK, so the castle isn't off the beaten path - at least not until after 5pm.
If you go later in the day, the light is much better, it's not too hot for climbing up the hill, there are no crowds and you can get into the Golden Lane for nothing.
The only reason to go during the day is to get into St Vitus' Cathedral and to see the inside of the palace.
The windows of the cathedral are wonderful (it includes one designed by Alfons Mucha). If you want to photograph them I recommend taking a tripod - we struggled without one.
The cathedral also has a tower that you can climb - it's 287 steps and quite hard work (!) but the views from the top are superb. It also provides a unique perspective because you get to see out to the west of the castle - a view that is blocked from anywhere else in central Prague.