There are so very many things! I recommend you request the most current copy of the Travel Oregon Visitor’s Guide, which will serve you for this trip and many others since it covers the whole state, region by region from local travel experts.
As a frequent traveler on I-84 between Portland and Pendleton, I wish I stopped more often at natural sights along the way: Rooster Rock State Park and Multnomah Falls are quick, accessible stops that let you pause to appreciate the Columbia River Gorge. Hood River is always a good stopover for food and drink. Doppio on Oak has coffee and lite lunch fare. Sixth Street Bistro is also a recommended lunch spot. If you’re driving through during the dinner hour, Brian’s Poorhouse and Celilo are sit down options with good wine lists.
Another great way to stretch your legs is to look out for kite board beaches between Hood River and Arlington and pull in to watch. I also recommend two natural areas: Deschutes River State Recreation Area, only a few miles off the freeway outside the Dalles (an important crossing point on The Oregon Trail) and McNary National Wildlife Refuge, which has hiking trails.
In Boardman, you can visit the state’s newest museum, the SAGE Center, slated to open in May. http://blog.oregonlive.com/terryrichard/2013/01/boardmans_interactive_sage_cen.html
If you’d like to jump off of the freeway to get a sense of the landscape along the Columbia Plateau, consider taking the Blue Mountain Scenic Highway. Exit I-84 to Highway 206 through Heppner to 395 and come in “the back way” to Pendleton.
Have a great road trip!