BUD VIE PRG doable and easy by train. If you can arrange it, fly into BUD and back from PRG, that way u only take the train in one direction.

I am like u, i love to walk around and explore. All of these cities are enjoyable. I like the Marriott in BUD for location and scenery, and the the Renaissance (i think now it is a Hilton) in Prague. Reasonable rates through hotelclub.net ot hotels.com.

Specific sites? plenty to do for a few days, just ask ur hotel staff for the latest info.