Not an expert about traveling with small children so keep that mind when reviewing what I say here.
We do have a website in Portland for parents with kids called PDXparents. One page of the site features Thing to do in Portland with kids that could be helpful.
Here are some places I know of:
The Children’s Museum – From what I have seen on this place it looks great. I wish they had this around when I would a kid. What I have heard from a couple of friends is that this place is grandma certified to take grand kid to to have fun. Only draw back is the cost.
Oregon Museum of Science and Industry – (OMSI) They have a couple of areas that are child friendly. At one time when I was being a guest grandpa I know Pager, temporary grand kid, loved the place. Not a cheap place.
Rose Garden Children Play Ground
Train Ride – At the Oregon Rail Heritage Center they offer a train ride to and from Oaks Amusement Park which can also be a good place for kids.
Trolley Ride – There is an old fashion trolley that runs from South Portland to Lake Oswego in the summer.
Tram Ride – Take the tram up to the medical school on the hill and enjoy the views and the experience.
See the animals – Oregon Zoo is designed for kids and families. Not a cheap place.
See the woods – There are possibilities of short hike up Balch Creek or Portland Audubon. Both have water access to the creek.
Go to the Beach – Kelly Point Park is where the Willamette River joins the Columbia River. We use to take Pager there to play in the sand by the river’s edge. If they go in the water keep a very close eye on that as there are hidden sudden drop offs.
Also check out the Portlant for Fun page. There may be some activities there that might be appropriate for older Children.
Here are a couple of clusters of activities you might consider.
Washington Park – Here you can combined the Oregon Zoo, Children’s Museum, Wold Forestry Center, Rose Garden, Rose Garden Children Play Ground and maybe a walk in Hoyt Arboretum. There are also picnic tables and green grassy places to play.
South East Water Front – An area to combine OMSI, Oregon Rail Heritage Center, a train to Oaks Amusement Park or a light rail ride over or a walk over the TiliKun Crossing bridge and the a tram right up to OSHU.