H.W.
ETA: double-check the dates for OMSI and some of the attractions; many are closed on Mondays. Not sure your littlest one would have much to do at Wunderland, either, but OMSI is great for keeping them busy and they have a little kids section for 6 and under. I'm sure they're open on Tuesday.
Jane,
Can you let us know how old your kids are, and how up they are for walking around?
Some things that pop up for me:
go online to Portland Parks and Recreation and use their "parkfinder" service; you can type in your general location and find parks close to the area you are staying in
http://www.portlandoregon.gov/parks/finder/
Down in the Pearl area (lower NW Portland) there's Jamison Square near 13th and Marshall or so: there is a great wading fountain which uses clean water and is okay for wading. Not a lot of shade on a hot day (the trees are still young), but very fun for most kids under 10 or so.
http://www.portlandoregon.gov/parks/finder/index.cfm?acti...
Downtown, around SW Park and Yamhill, there's Director Park, which also has a wading fountain. Again, not a lot of shade. On Wednesdays, you can toodle down a block or so to Salmon (on the Park blocks) and hit the farmer's market for some nice goodies. They're usually there from 10-2 at Shemanski Park (what that park is called). On Monday, the Farmer's Market is also a couple blocks away at Pioneer Square from 10-2.
Take the MAX to Washington Park and take the elevator up to daylight (the stop is in a cool tunnel)... if you have some fun money to spend, consider the Children's Museum or Oregon Zoo. At the Oregon Zoo, if you want to splurge, there's the Zoo Train which does a loop over to the Rose Gardens: you can get off there, walk around, and re-board back to the zoo on the same ticket.
http://www.oregonzoo.org/
http://www.portlandcm.org/
In Old Town, the Classical Chinese Gardens are a treasure. Contained in one block, the Scholar's Garden has a pond with koi, neat little alcoves and lots of wonderful, beautiful details. They also offer a 'kids guide' as well.
OMSI. (Oregon Museum of Science and Industry) On the SE side on the Waterfront. Spendy but my guess is that you could spend a good chunk of the day there, and they have space to eat food you have brought in yourself as well as a cafeteria if I remember correctly.
For cheap fun, check out any of the Wunderland nickel arcades. Their website offers a coupon, too, as well as locations and hours. This is a constant favorite for our son and many of his friends.
http://www.wunderlandgames.com/
Portland has some great walking tours and the Visitors Center at Pioneer Square has lots of brochures. We've done some Fountain Walks (checking out the various public fountains) and there's also a public art guide.
http://www.portlandoregon.gov/water/article/225489
http://www.travelportland.com/things-to-see-and-do/pdfs/p...
This might help, too:
http://www.travelportland.com/things-to-see-and-do/attrac...