We were at Mt. St. Helens (actually in Washington but not far from Portland) in early July a few years ago and visibility was poor though precipitation was light. Impressive, even after all these years of recovery, the overwhelming power of nature and how it shaped the landscape to its own mold. At least one visit is a must do for any trip to the area. Be aware that you may need permits/reservations for some hiking and camping activities. Mt. Hood would be my other but there are also some coastal trails of spectacular interest.
There are three access routes with trailheads originating at each:
The western access leads to the Johnson Center, HQ of this national monument with a very educational visitor center and all the information you will need to explore the place. Be aware that not all parts of the monument are open at all times. I believe one area may have been closed for a while because of some modest volcanic activity. The road in to the Center, when visibility allows, overlooks the river valley and how it was reshaped by the volcano and ensuing mud flows and floods. Great swarths are littered with downed trees which appear from above like so many matchsticks, 'til you see them up close.
The southern access is the best way to get to the trail that goes along the rim of the caldera. The risks along parts of this trail are not trivial.
The northeastern entrance, furthest from Portland, takes you to several trailheads, at least one route skirts the edge of the mountain that was blown away and other routes pass through pristine areas that it seems like the eruption missed. I think just about every trail will give you views and upclose acquaintance with natural forces you will not forget.
We did some short hikes at Mt. Hood just to get our feet on the ground as we passed through but there was still significant snow on many of the trails.
We camped in a yurt at Cape Disappointment, a Washington State Park, about 100 yards from the Pacific Ocean which, from the din even at a distance, hardly seems pacific. For us, this was a stop on the Lewis and Clark Trail, most of which we covered in two extended roads trips but with still some sections to explore further in western Montana and Idaho.
The hikes we did along the coast were also short ones, again in passing as we headed to San Francisco. These trails overlook the ocean and sometimes include beach walks past shipwrecks and seals. Ft. Stevens SP offers several possibilities. We didn't get to Silver Falls SP but there are falls and a historic lodge; 10 Falls Trail sounded inviting and, as the West goes, the park is not far from Portland.