On your second morning in Portland, rent a car and drive east into the Columbia River Gorge. This is truly one of the natural wonders of the world and words fail me to describe how grandiose and breathtaking beautiful it is. You'll just have to see it for yourself.
I strongly recommend driving on the Historic Columbia River Highway rather than on I-84, for a fittingly relaxed (and more interesting) driving experience. There are several places where you'll want to pull off the road and see the sights, most notably Multnomah Falls, but also Vista House (which looks to me like a structure out of Myst) and Bridal Veil Falls. Be warned that the traffic around the parking lot for Multnomah Falls can be absolutely brutal; I had to park at the Wahkeena Falls pulloff about half a mile back and walk.
It's fascinating to watch the land change as you drive east along the Columbia; the farther you go, the trees get shorter and the grass yellower. This effect becomes noticeable quickly east of about the Bridge of the Gods. In addition to having a cute downtown, the town of Hood River makes a good place to stop for lunch; I grabbed a quick beer at pFriem Family Brewers. Hood River is a popular place for wind surfers because the Gorge acts as a giant wind tunnel; it was extremely windy on the riverbanks while I was there. The area also offers spectacular views of Mount Hood, directly to the south.
I continued a little further east, to The Dalles (rhymes with "pals," does not sound like "Dallas"); one more good place to pull off in this stretch is the Rowena Crest Viewpoint. I wanted to cross the Columbia at The Dalles rather than Hood River both to see the full effect of the landscape change (you're well out of the Cascades by then) and because the bridge at The Dalles is free and the one at Hood River is not (and does not take credit card). Of course, you could not cross the river at all and double back the way you came, but where's the adventure in that? So anyway, I crossed into Washington State and headed back west toward Portland. The Washington side is just as pretty, though with fewer sights to pull off for, save for Beacon Rock.
I arrived in Vancouver, WA (across the Columbia from Portland) just before closing time of Fort Vancouver. I slipped in and saw what there was to see. Pretty neat. I walked around the downtown a little bit and noticed the very interesting but derelict Providence Academy building. Then I drove back across the river for another dinner and night in Portland.
As a pro tip, parking at any hotel in the Pearl District is going to be quite expensive. Parking on the street is less so, or free if you're willing to walk a little ways. I rented my car from Enterprise on West Burnside and parked very near there (across from the cathedral, as I recall). It was about a 10-12 minute walk from my hotel and parking was free for the night. Just watch the signs carefully; it's fairly clearly marked where is free to park and where is not.