Good to write something not about football....
It's a great place to visit in my opinion. As others have said not too many sites as such but you can visit some nice countryside, have good food and enjoy the welcoming atmosphere. I always feel it is as at least as much Japanese as Chinese which is not surprising since it was a Japanese colony for quite a while. It's also got a big American influence (they like their baseball). I always think it is what Singapore could have been/be with better politicians. The people are chilled, quite artistically minded, well mannered and educated. I recommend Taroko Gorge on the East coast, Yangmingshan near Taipei, Jiufen near Taipei, Sun Moon Lake and Taipei of course. Got to have beef noodles, go to Din Tai Fung, eat at a night market and have a bubble tea! I think it is good for maybe 8-10 days in total.