The whole of the "mainland" of Taiwan is easily accessible by bus/rail and internal flights aren't really necessary unless you want to visit the outer islands such as Kinmen, Matsu, the Penghu archipelago, Green Island or Lanyu.  Whilst ferry service are available to these islands, the seas around Taiwan can be fairly tumultuous, so you may prefer to fly.
 
The whole of the "mainland" of Taiwan is easily accessible by bus/rail and internal flights aren't really necessary unless you want to visit the outer islands such as Kinmen, Matsu, the Penghu archipelago, Green Island or Lanyu.  Whilst ferry service are available to these islands, the seas around Taiwan can be fairly tumultuous, so you may prefer to fly.
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Airlines such as Daily Air Corporation fly to Lanyu and Green island.
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Main airlines flying to the outer islands are:
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