Banqiao's Lin Family Mansion and Garden (http://www.linfamily.ntpc...) is one of the best examples of Qing era Chinese architecture in Taiwan. It is free of charge this was formerly not the case, but was as of June 2012 and well worth a visit.
Danshui Fisherman's Wharf is New Taipei's most famous scenic sight.
Enjoy your coffee or tea beside the Bitan Lake, Xindian.
Jiufen is famous for gold mining. There is an excellent gold museum.
In Fulong, you will find a coastal district with an excellent beach. Every July, don't forget to attend the three day Ho-hai-yan Rock Festival.
Enjoy the aboriginal Dancing show and hot spring in Wulai.