What a fun question! Here are my top recommendations.
Memorial Park in Wilsonville. This would be a really easy stop for getting on and off I-5 and a great place to get out and stretch your legs. Heading south from Portland, you’d just take exit 283, then head east for 1 mile. Memorial Park is in the middle of the Portland suburb of Wilsonville but the park itself is big (126 acres) with picnic areas, trails, a creek and even some frontage of the Willamette River. I lived near there several years ago and my kids’ favorite thing to do in the summer was walk to this park and play in the splash park on hot sunny days. (It has covered picnic areas for not-so-sunny days too.)
Champoeg State Heritage Area. This one is about 11 miles west of the freeway, but it’s a really lovely state park. It’s not only in a very pretty area alongside the Willamette River, it also has some very cool historic sites you can visit that might be fun for breaking up your journey. If you go during the summer you can stop and get an ice cream cone at the historic Butteville store, the oldest continuously operating retail establishment in Oregon!
Bauman’s Farm & Garden in Gervais. A farm and garden store might not seem like a great place for a picnic, but this one is. Bauman’s Farm is a family-owned farm, nursery with an on-site bakery and farm store. Their bakery is to die for and they have places to sit down. Buy a homemade cookie or donut to go with your picnic, or in the summer buy fresh produce to enjoy. They’re open year-round, and they’re only 5 miles off the freeway.
Willamette Mission State Park is a peaceful state park about 5 miles west of the freeway. It’s mainly a nature preserve with plenty of open area for picnicing and trails you can walk on. Depending on how much time you have, you can also take a ride on the Wheatland Ferry, which takes cars and people back and forth across the Willamette River at a crossing adjacent to the park. Its’s one of a handful of river ferryboats that are still operating in Oregon. You can just ride over and back, either on foot or with your car, for the fun of it (and for a nominal fee) even if you don’t have a pressing matter on the other side. My kids think riding the ferry is fun, but maybe they’re just easily amused!
If you’re into wine tasting, you might also try having your picnic at Arcane Cellars instead of Willamette Mission State Park. Arcane Cellars is just across the river from Willamette Mission State Park and the Wheatland Ferry. It’s family-owned by friendly folks and they make great small-batch Oregon wine. They have a tasting room, a covered patio area and picnic areas for visitors. They also have a very charming winery cat who greeted me when I visited there. If you visit on a weekday that’s in the off season (i.e., not the summer) you will want to check with them to verify that they’ll be open, or make an appointment. Like many small Oregon wineries, they have limited hours during the off season.
I hope you have a pleasant drive and find a good spot for your picnic. Enjoy your visit to the Willamette Valley!