This water park and museum is situated right behind Gongguan. The park I am describing here is the public one, not the large private spa that is next to it.
The water park area is great for kids, as the water is really shallow. There is a playground in the middle of the pool which is constantly spraying out water, so if kids are afraid of getting water in their eyes, its best to take some goggles. If your kids are really little, they can just play in the small pools at the entrance.
If you don't want to take your children swimming, you can do the easy walk up to Taipei's first water reservior, and let them run through the water pipe display. There is also a museum that is fairly "hands-on", letting children learn a little bit more about where their household water comes from.
The best things about this place are, it's cheap, it's easy to get to, and it's got lots of different things to explore.
The official English-language site has lots of information: