It's good for mountain biking, or even off road touring, but mixed for road cycling.
There are a few forests in the city itself (Kunraticky Les and Divoka Sarka) which have loads of paths going through them - loads of cycle routes in Prague as well, there's a map you can get for them.
For road cycling, you have to pick the routes carefully to avoid the motorways and really busy roads that run around the city. There is a nice route out along the river in both directions, and there is a route called the Prague Circle which is about 160km and runs around the outskirts of the city on minor roads - its pretty up and down, and you can join it at several places by catching the metro.
Regarding the Czechs, their attitude to cyclists is pretty good, but not as courteous as in France/Spain. Nearly everyone, even people who cycle on the roads, use mountain bikes.