The other folks have given you good suggestions if you head over to the coast; I can affirm all of them. In regards to heading the other direction, into the Cascades, a good choice from Eugene would be the "Wild and Scenic"-designated upper McKenzie River, above McKenzie Bridge. A good plan would be to access it from various points along the McKenzie River Trail, which runs close to the river for about 26 miles. Its closest point to Eugene can be reached in about an hour, near the Willamette Forest ranger station.
For instance, check out Sahalie Falls, right off Hwy 126. The falls are spectacular. And from there you can walk a very scenic loop: follow the path upstream for about 1/4 mile to a footbridge, cross it and then walk downstream on the McKenzie River Trail for about 1 mile, to a bridge spanning the river above Carmen Reservoir. Cross that bridge, and walk up the path on the east side of the river back to Sahalie Falls. I'm confident you won't be disappointed--stunning views of the clear, blue rushing water, seen through old growth rain forest.