There is a Jurys Inn just up the street from my apartment offering tremendous room rates right now. From there, you can easily walk or catch the #8 tram to Namesti Republiky. If you're taking the tram, stop at a Tabac and buy a Jizdenky (ticket) for the day.

From Namesti Republiky, you can very easily walk to Stare Mesto (Old Town). From Stare Mesto, you can easily walk to Malestrana. From Malestrana, you can take a tram up to the castle.

The city is made for walking and all of the best parts are relatively close to each other. I walked from Malestrana all the way to my apartment in Karlin one day in light snow. It's not difficult at all. The streets and sidewalks are cobblestone so wear sturdy shoes.

And, as has been stated here before, the women are lovely. Just keep your wallet out of your back pocket. Otherwise, the city is incredibly safe. My wife and I walk almost anywhere at night without worry.