If you haven't had the chance to go to Sun Moon Lake in Taiwan, this could be a great reason for a first visit. It hosts an annual 3-km race across the lake, where swimming otherwise is forbidden.
The lake is surrounded by mountains and the whole area is generally amazing. The only potential downside is how time-consuming it is to go there. The easiest way there would probably be on a bus, directly from Taipei. The fastest would have to be by taking the high-speed railway from Taipei to Taichung, followed by a bus-ride. Oh, and they have apparently had tens of thousands of participants in recent years, so it might get crowded.
There are also bicycles for hire, that you can take around the lake, which is something I definitely recommend.
Sun Moon Lake Swim http://news.xinhuanet.com/english/photo/2013-09/08/132702616_21n.jpg
Source: http://news.xinhuanet.com/english/photo/2013-09/08/c_132702616.htm