Start in Prague – the country's highly atmospheric capital is more child-friendly that you might have thought. Prague is located in Central Bohemia, where castles and old silver mines are the big draw for kids.
Discover the rest of Bohemia (West, North Bohemia, East, South, and the Bohemian-Moravian Highlands), which accounts for much of the country. In South Bohemia, Český Krumlov is a gem of an old town with a UNESCO-listed castle. It's close to Šumava National Park, the Czech Republic's biggest, which attracts walkers, cyclists, and canoeists. Or head for north-east Bohemia and Český Ráj ('Bohemian Paradise'), a protected landscape with 'rock towns' formed by sandstone cliffs and volcanic basalt rock 'fingers', plus a couple of dramatic ruined castles. Hiking and biking trails help you to discover it. The nearby Krkonoše ('Giant') Mountains, the country's highest (shared with Poland), are home to the Czech Republic's most popular ski resorts, most notably Špindlerův Mlýn.
Explore the Moravia region, home to pretty vineyards and orchards, scenic mountains and sweet villages, and a charming regional capital, Brno, where sights include the Technical Museum with its hands-on Experimentarium. Telč has a UNESCO-listed town square bordered by well-preserved Renaissance and Baroque houses plus a 17th-century Renaissance chateau with an English-style park, all surrounded by shallow artificial lakes. In the Moravský Kras karst area between Brno and Olomouc, the Punkevní Caves offer you the chance to marvel at the Macocha Abyss and take a boat-ride along an underground river. Southern Moravia (near the border with Austria) is a particularly lovely spot for cycling, with lots of well-marked paths through a countryside chock-a-block with vineyards, wine cellars and cutesy villages.
Get hold of the Czech Tourist Club (Klub českých turistů) walking maps, covering thousands of kilometres of scenic paths around the countries. They're available in most bookshops and museums as well as online.