Taipei's Coolest Museum: The Miniatures Museum of Taiwan
The Miniatures Museum of Taiwan is a great stop for those with children who can appreciate such a museum. There are tons of displays but a great deal of variety, so it's difficult to get bored easily. And others can enjoy the museum as well - modelists and train hobbyists, for instance (though there aren't really any train displays, those who create realistic town and country layouts would enjoy it).
Open from 10-6 except for Mondays, the museum is a short walk (about 6 minutes) from Songjian Nanjing Station on the metro line. I ended up taking taxis to and from the museum to save time because the locations I came from and went to weren't easily accessible by other forms of transportation, and the weather and time weren't on my side. There's a nice gift shop with plenty of dollhouse furniture and other miniatures supplies and souvenirs.