I stumbled across the open-air sandpit next to Taipei City Hall (Hsinyi District, Taipei) when we walked from The Discovery Center Taipei to The Hsinyi Eslite building (great kids' bookstore). It is a fairly large sandpit running along a length of sidewalk, with a wooden boardwalk and outdoor tables and chairs. There are three watertaps with soap to wash the kids off after they play. The sand is very clean. It's a kind of man-made sand so it is white and the granules are larger than the sand usually found in sandpits. This time of year (Feb/March) is perfect for this area. It is uncovered, so I imagine it must be very hot during summer. You need to take your own sand toys (although my kids did manage to convince other parents to share their sets with them). Children were improvising with old coffee cups and laundry detergent spoons. It was surprisingly quiet when we visited. There are no cheap convenience stores close by, so you best prepare your own drinks and snacks. Take a book and put your feet up while your children play.
I am trying to find a street address for this sandpit but I am not having much luck. It is at the south-east side of Taipei City Hall. (No.1, Sh fu Rd. Xinyi Dist, Taipei City)