My friend & I are going to visit Taiwan very soon, we'l be arriving at Taoyuen airport on 4, July 13

We have already booked with Dong Wu hotel for 5 night stay there, my concern since we wil be staying in hotel in Taipei, beside Taipei any other cities (such as Taichung, Hualien) that we can travel to within the same day in order to go back to Dong Wu hotel on the same day? Thanks.