I don't know much about the Czech Republic other than Prague. I've been there a lot, but other than that, I haven't seen much. I've driven through, and stayed in Plzeñ.
Read about the Czech Greenway, a great set of trails from Prague to Vienna!
In Your Pocket makes the best city guides for central Europe and the Baltics. They are smaller, cheaper, wittier, and more up-to-date, than the big guns. Ask for them in kiosks in Prague (they are often not displayed) or download the free abbreviated versions right here:
Sedlec is a small town outside of Kutna Hora, which you can get to in about an hour on the train from Prague. Just off the main road into Kutna Hora, there's a small chapel, set in a very green graveyard. There is a statue of a Saint outside, with a halo of stars made from gold metal. There's a low-key, local restaurant opposite. The church-yard is quiet. The church itself has spires, and at the top are skull and crossbone motifs.
Sedlec is not actually a church - it's an Ossuary: a tomb. Inside, it contains the remains of about 40,000 people. They have been used to decorate the building: their skulls cover the walls, their limbs hang from the ceiling as a massive chandelier and their bones form a huge coat of arms on one wall. I spent an afternoon in the place and have loads of creepy photos up on my site.
Don't miss Church of St. Barbara in Kutna Hora (near Sedlec). It's one of the best European catherals.
Buy Lonely Planet Czech & Slovak Republics.
A great guide for someone visiting either of the two countries. If you are just going to Prague, there are city guides available.
Buy Eyewitness Prague.
Eyewitness travel guides have hotel and restaurant information, but their real value is found in the history, and the beautiful, detailed illustrations giving you a deep sense of where you are and what has come before you.
Buy Prague: A Traveler's Literary Companion.
A collection of 23 Prague related stories in English. A great way to add more meaning to your Prague trip.