There is superb climbing in Taiwan, but the rock climbing is not as abundant as this very mountainous island would seem to offer. Of particular note are the beautiful sea cliffs of LungTung (Dragon Cave), Taiwans premier rock climbing area. If you are in Taiwan, LungTung is a must stop on any climbers itinerary. (LungTung is located above the p in Taipei on if you look at Mapquest.)
Mountain hiking is an enjoyable activity on this subtropical island. The highest peak, Jade Mountain, is 3952 meters tall and there are over 100 peaks above 3000 meters in height.
Along with LungTung, there are other rock climbing spots around Taiwan and probably hundreds of unclimbed cliffs. Climbing could be developed on the off-shore island of PengHu as well (basalt cliffs on the ocean).
Have a look around here at some of Taiwans climbing possibilities. But if you are headed this way, be sure to at least bring your shoes and harness. You can probably find a friendly local climber willing to show you around.