Just Walk Backpacker Hostel--I highly recommend! There was only one other lodger there the nights I stayed. The owner of the hostel was incredibly accommodating and provided a map with recommendations for the best restaurants in town and attractions around the city as well.
Dongdamen Night Market:
A quite small, average night market but still worth checking out! The pork buns and roasted corn are noteable. Many Indigenous stalls that can't be found elsewhere in Taiwan.
Taroko National Park--I recommend going through a tour group. I chose The Better Taroko National Park Tour with Island Life Taiwan. Great tourguide, small group, many photos, and visited all of the top hits of the park without a lot of tourist traffic.
Another way to do Taroko is to simply rent a motorbike or scooter yourself. It gives you the freedom and flexibility to go at your own pace and visit any places you'd like.