sis yby2476 - yeah I've seen that magazine but everything is still in Chinese... if you're only after the pin-ups and photos, then it's ok ;-) just as long as the requirements submitted are complete, you'll get a single-entry visa naman.
About places to visit... there are some nice places like:
Jiufen - inspired the movie "Spirited Away"
Yehliu - Queen's head rock formation
Taipei 101 - 2nd tallest building in the world
National Palace Museum
Sun Yat Sen memorial hall
Chiang Kai memorial hall
Taipei zoo
Maokong Gondola - cable car
Danshui
Martyr's shrine
Beitou hot springs
Night markets (Shilin, Raohe, Ximending, Shida)
Temples (Longshan, Match-maker)
Wulai - trekking
Bitan - cycling/boat cycling
(Outside of Taipei:)
Sun Moon Lake
Taroko Gorge
Alishan mountain railway
Kending
Kaohsiung spots (there's a lot but I'm not too familiar because it's in the south na)
I think most people come here for the night market experience and the food