If you don’t regularly use these, you can convince your child that a ride on public transit is almost as good as Disneyland!
For the bus, plan a short simple outing at non-peak travel times, and get a transfer when you board – you’ll be able to ride back out for the single fare. Focus on enjoying the journey, not just the destination.
On light rail or Sounder rail, you can go on a scavenger hunt for the public art at their stations: see http://www.soundtransit.org/Rider-Guide/public-art. (Also, check out this great article, which is focused on light-rail-based adventures, but also has plenty of “cheap date” ideas for downtown Seattle: www.deliciousbaby.com/journal/2010/jan/13/seattles-link-light-rail-kids/