Portland to British Columbia

If you are interested in spectacular coast line, Oregon has more to offer than Washington.

If you want to include the Oregon coast, your routing might be (1) Columbia River Gorge, (2) Willamette Valley wineries on way to the coast (3) Highway 101 from Cape Perpetua to Astoria, (3) Olympic National Park, (4) San Juan Islands for kayaking and whales, (5) Mt. Rainier, (7) Portland.

If you don't want to see the Oregon coast, you might instead visit Victoria BC by ferry from Port Angeles.

HTTY

I agree with HTTY that you'll have a better coastal experience in Oregon than in Washington. The 2 bridges across the Columbia that will impress you are the one at Astoria and the Bridge of the Gods at Cascade Locks. http://www.portofcascadelocks.org/bridge.htm
Olympic NP doesn't have any "through roads". Consider seeing Mt. Rainier and Mt. St. Helens.
Why not fly to Seattle and rent there? If you only want to visit Vancouver BC, ride the Amtrak train or bus from Seattle.
Don't forget your Passports.

Hmmmmmmmmmm... sometimes it is easier to take a shot at answering when there are perhaps two or three MUST-sees as described by the O.P.

But ok, just working with "flying into Portland" and including the Columnbia River Gorge...

Given what others have added, it probably makes the most sense to do a "loop" of Oregon, perhaps going first to the coast... then driving down as far south as you want, before cutting to the east, bypassing Interstate-5, and continuing east, eventually to Hwy 97, running north to south through "Bend, OR".

IF you go far enough to the south you can make Crater Lake convenient to you... and then on the way north you might do well to take Hwy #26 from the town of Madras, for a close-up encounter with Mount Hood. After that, go to Hood River and maybe cross to the Washington side for at least one side of the up-and-back viewing of the gorge.

As an alternative to Interstate 5 between Portland and Seattle, consider the path between tiny Carson, WA and Packwood, WA. I was surprised to find such a path via 'Bing Maps' a year or two ago, but it would give you lots of nature, and mighty Mount Rainier would be right in your face upon arrival on the other side. (with Mt. St. Helens not far off the path as well)

From Randle/Packwood, WA... you could drive around the east side of Mt. Rainier on your path into the Seattle area.

Since by then you would have availed yourself of a good dose of the Oregon Coast, I think perhaps you could forego the Washington coastline and instead afford yourself that journey to BC.

Head for Vancouver first... and near there you can make a day trip to see Grouse Mountain, which would combine "breathtaking views" and "short hikes" of your choosing. (if you time it ideally, you get there during the day for whatever outdoor stuff you want to do (I.E. hiking)... and then straddle sunset to see the views after dark)

Clarity: grousemountain.com... and it costs $40.00 PER PERSON to ride a gondola up the side of a mountain, from just outside of central Vancouver, with restaurants and hiking and scenery and souvenirs at the top.


I know you cited 10 days for your journey..., and eventually you'd need 5 hours of driving time (plus traffic both in Seattle/Portland, AND at the border from Canada) to go 315 miles back to Portland (from which I assume you'd fly home).

Obviously there is a whole lot to do in Vancouver, but I'm just throwing this out there now, and would add Vancouver detail IF it seemed to interest you.

Alternatives include the North Cascades Highway in northern Washington (I drove it last summer, and some of the scenery there is stunning).

Hope this helps somehow.

IF you do decide to come to Bend (or Sunriver), there are several places to rent tubes or kayaks to go on the Deschutes River or any of several High Cascades lakes.
http://www.visitbend.com/Bend_Oregon_Activities_Recreation/Outdoor-Recreation/Summer-Fun/Rafting-River-Activities/