What are the best places for a tourist to visit in Taiwan?

TAIPEI CITY

National Palace Museum http://www.npm.gov.tw/en/home.htm

Sun Yat-sen Memorial Hall

Chiang Kai-shek Memorial Hall

Taipei 101 area http://taipeiguide.blogspot.com/2006/05/taipei-101...

The 2010 Taipei International Flora Exposition (6 Nov 2010- 25 Apr 2011) http://www.2010taipeiexpo.tw/MP_4.html

Maokong & Maokong Gondola

Taipei Zoo (my favorite animals: pandas & king penguins)

Shilin Night Market

New Beitou

TAIPEI COUNTY

Danshui http://wikitravel.org/en/Danshui

Yeliu Geopark http://en.wikipedia.org/wiki/Yehliu

Jiufen & Jinguashi

Shifen & Pingxi

Wulai

Yingge

NANTOU COUNTY

Sun Moon Lake Scenic Area http://www.sunmoonlake.gov.tw/sun.aspx?Lang=EN

CHIAYI COUNTY

Alishan National Scenic Area http://en.wikipedia.org/wiki/Alishan_National_Scen...

PINGTUNG COUNTY

Kenting National Forest Recreation Area http://eng.taiwan.net.tw/m1.aspx?sNo=0002122&id=68...

HUALIEN COUNTY

Taroko National Park http://en.wikipedia.org/wiki/Taroko_National_Park

KINMEN COUNTY

Kinmen

Please GOOGLE each place for details.

I'll suggest Taroko Gorge National Park on the East Coast of Taiwan. Just getting TO it is a pleasurable experience.