What will be your flight schedule? if it's morning flight to Taipei and evening flight back to HK, you may try it this way:
Day 1: 淡水/漁人碼頭 + 士林夜市
Day 2: am to 野柳, pm to 九份, dinner at Keelung/饒河街夜市
Day 3: 木柵動物園 +中正紀念堂 (if there is time) +鼎泰豐
Day 4: am to 故宮, the rest of the time in 西門町 (阿宗面線)