Honestly Taiwan is great all year round. We are not overrun with tourists (yet) so even in the high season it's not too busy, especially outside of Taipei
But if I had to pick a season, I recommend visiting in the fall.Late September-November are perfect weather-wise in Taiwan. Daytime temperature is 20-25 degrees celsius (68-77 fahrenheit) in these months and rainfall is pretty low. You get lots of mild sunny days perfect for exploring the country
Spring is also great, April-early June. Temperature is also in the 20-25 degrees range but there's more rainfall than fall
Summer gets too hot for some people as temperatures can get to above 30s (86 fahrenheit) and winter gets cold for some people (night time temperature goes down to around 12 celsius or 53F)