Where to go
We don't recommend you biking in Prague - there is a pretty heavy traffic and no bicycle paths so there is not much to enjoy. If you need to start or finish there, your might escape from the city center to the suburbs by underground.
The most of the rest of the country is suitable for biking and nice. South Bohemia is flat (full of ponds, forests and nice), the border with Germany is pretty hilly, and the rest of the country is more or less varied.
What to see
Apart from Prague, there are many nice small towns with historical centers, e.g. Cesky Krumlov, Telc (both on the UNESCO world heritage list, another item from this list is the Pilgrimage Church of St. John of Nepomuk at Zelena Hora in south Bohemia), Kutna Hora (an old town, in the Middle Ages of about the same importance as Prague, with a nice gothic cathedral and some other nice monuments), Tabor, Litomerice, Slavonice etc. There are also many castles open for the public, for ex. Pernstejn in South Moravia (a well-conserved Middle Ages fortress), Karlstejn near Prague (Middle Ages, too, but very familiar at many tourists, so you cannot avoid crowds there), in South Bohemia a water castle Cervena Lhota and the castle in the town Jindrichuv Hradec and many, many more. The landscape is nice, too- forests, ponds, small villages etc.
Trains
The train is a good access possibility if you want to take the bike with you as well as if you want to travel within the country. On all bigger lines, the bike transport is possible in about 50% of trains.
Guided Mountain Bike Tour - covers some of the most challenging terrain between Prague and Vienna on a mountain bike.
MTB page by Zdenek Bartos
Guide 
