The Heritage and Culture Education Center is good for children roughly 4 to 10 years old, for a couple of hours. Asiababy wrote about it here: http://kidzone-tw.blogspot.tw/search/la ... %20Centers
It's basically a child-friendly museum about old Taipei. I found it quite interesting, too. There's an article here: http://taiwanreview.nat.gov.tw/fp.asp?x ... ctNode=205
Closest MRT station is Longshan Temple.