阿崔,
If you go to Taipei only, I would recommend 台北植物園 where you can see Malayan Night Heron very close to you! I have also seen Black-naped Monarch, Brown Shrike, Black-browed Barbet (五色鳥) and Grey Treepie there during my visit to Taipei last November. It is a park just like Kowloon Park in HK. You don't need to walk long distance to find birds and you can ask birders there and they are very kind to bring you around to look for birds. It is a great place and Taiwan birders are nice too!
Taiwan birders also recommend 烏來 which is a sea-side forrest area. I haven't been there. But they said it is also a good place during migration period. Just like Po Toi, they got a number of rare birds and even "first" there. You can have a try.