After spending a few days in Taipei, we took the train to Taroko National Park for two nights. Since it was Lunar New Year, we had booked train tickets in advance. The website was not very user friendly and was very glitchy! I think you'd probably be fine just buying them at the station. The train ride from Taipei to Hualien (close to the park) was about two hours and cost only about $15. Amazing!
We stayed in Formosa Backpackers Hostel. We rented a scooter which made it a lot easier to get around the park. We spent a full day at the park and did the Swallow Grotto Trail and Baiyang Trail (both very easy). I read that the Shakadang Trail and Tunnel of Nine Turns Trail are both supposed to be great too!
At the end of Baiyang Trail, there is a man-made tunnel that has water gushing from the ceiling. According to the Taipei Times, while a power company was making the tunnel, they hit an underground water vein, hence the gushing water. Since the area is at risk for rock slides, there are signs everywhere telling you to enter at your own risk. I get super anxious about these type of things, but once I saw elderly women going in, I figured I could too. It was really neat (see a photo here) but I was so happy once we were back out! :)
We also checked out Xiangde Temple and drove to Qingshui to see the cliffs. It started raining at that point, so our view was not the best (also made for an interesting scooter ride!).
At night, we were pleasantly surprised with how much there was to do in Hualien! We went to Rainbow Night Market and Cultural and Creative Industries Park. We also had a very non-traditional Taiwanese dinner at Salt Lick (American barbecue!) - so good.
Next up - Ximending and Chiang-Kai Shek Memorial Hall in Taipei!