Taipei, Taiwan is quickly becoming a world leader in urban biking.
Already a world leader in bike manufacturing the biking industry has taken hold of the popular imagination and bike lanes, bike trails, and urban riders of all sorts are on the roads.
The northern suburb of Tienmu is surrounded by a national park, Yanmingshan National Park, a mountain park with mountain roads, hot springs, incredible vistas, waterfalls. The roads are usually lightly travelled and now have ample riders at nearly any time of day. http://en.wikipedia.org/wiki/Yangmingshan
The city government is also finishing a series of urban bike trails along the rivers in town so you can bike for over a hundred kilometers without crossing a road. Going from downtown, Taipei 101, the zoo, the world trade center, out to Danshuei and the North Coast without hassle.
In Taipei, there are plenty of family bikers, road bikers, casual bikers and now we are even seeing more bike tourers You can circumnavigate the island in a couple of weeks. There is some great mountain biking for the technical mtn bike set.
The roads are still a bit crazy. Lots of cars, but traffic doesn't move so fast as to threaten bikers. Their are scooters all over which can be a bit disorienting. But it is improving regularly.
There are also so many great bike shops in town....from high end racing bike to low end foldable bikes.
Taipei is a biker's dreams.