If you’re traveling with children, the National Taiwan Science Education Center has tons on offer. Interactive exhibits at this children's museum cover the gamut of scientific knowledge, from anatomy (a walk-through digestive tract) to zoology (a cat-head-shaped helmet that gives the wearer feline hearing powers) to chemistry, life science and physics. There are good English translations at every point. It also pairs well with a trip to the Taipei Astronomical Museum which is just across the road. Note that the 3D theater (turbo ride and regular), sky cycling and special exhibits are not covered by the general admission ticket.
You can take the R30 bus from here straight to the National Palace Museum or Jiantan MRT station.