Based on a one week trip in the mid-90s and a several day trip in 2003.
Prague is definitely one of the great cities in Eastern Europe. The historical old town with all its beautiful buildings is so extensive that you almost feel like being in one big museum. Avoid the main tourist seasons, since the whole place seems a bit artificial is there are crowds of camera-clicking tourists around you all the time. You may also want to explore less touristy parts of Prague to get a more real feel for the city.
Sumava National Park near the German border forms one large conservation area with the Bayerischer Wald National Park in Bavaria. The Czech side is much emptier and less developed than the German side and consequently feels more like a wilderness (there are still wolves in this area). We did a cross-country skiing tour through Sumava National Park which was absolutely great: a true backcountry experience with almost no developed pistes, hardly any people and very little tourist infrastructure.