Have lived on the west coast all my life...
As has been mentioned, head east along the scenic route for the Columbia River Gorge (you exit from the freeway as you leave Portland). There are several fabulous waterfalls along that route, Horsetail and the well known Multnomah Falls, to name two. Crown Point has a nice vista of much of the gorge.
Astoria is good, or take just about any of the two lane roads over from the valley to the coast. A stop at Gold Beach is another option, the sand dunes at Florence might be of interest, and Depoe Bay is a very tiny and quaint place. On the way back, if you take the route from the coast back to Grants Pass, a stop at the Oregon Caves could be fun (one of the larger cave networks outside those at Carlsbad, NM. Overall, IMO, US 101 is far more scenic that I5. If you like Victorian architecture, the Carson Mansion in Eureka is worth a look. Jedediah Smith Redwoods and Redwoods National Park, as others have mentioned, are almost "must" stops. If you like more-or-less dirt roads, consider taking a detour to fern canyon on the coast. Also if it still exists, Lazio's in Eureka has very good seafood. Crater Lake is futher east than it sounds like you might be going. Bend, on the east side of the Cascades is a jumping off point for much of the scenery in eastern Oregon. If you like wading in the ocean, the beach at Seaside is unusual for a west coast beach in that you can wade quite a ways out into the ocean. Note that Seaside and Cannon Beach are popular tourist places.
As for "rain forest" you would need to head north up to the Olympic Peninsula. The Olympic Peninsula is unique in that it contains a temperate rain forest. The Hoh River Valley averages something like 175 inches of rain a year. IIRC, the only town in the area is Forks (sorry, no town named Knives or Spoons).
Anyway, have fun.