Hi,please suggest the best time to visit taipei and whats the best things to do in Taipei?

Generally speaking, October to May next year is regarded as the best time. It won't be the typhoon season. And the climate would be cool and comfortable. The several rainy days won't influence the sightseeing a lot.
If you have enough time, you are advised to tour around Ali Mountain, Mt. Yangming, Jade Mountain (Mt. Yushan), Sun Moon Lake and Taipei National Palace Museum.