Being from Washington, I’m partial to the ‘local’ part of the trail. That said, I truly think the northern most sections are some of the most spectacular.
If you had 2 weeks and can do good miles right off the couch, I’d suggest starting at Snoqualmie Pass and heading north to the finish - you should be able to do it in 14 days, although 16 to 18 would be more comfortable.
Getting to Snoqualmie from Seattle shouldn’t be too hard - public bus to North Bend and hitch the remaining distance. From Manning, take the greyhound to Vancouver BC and from there either bus or Amtrak back to Seattle for your flight home.
It’s not two weeks, but I’ll second the Goat Rocks (Do Cascade locks to White Pass - ~147 miles). You get up close and personal with Mt. Adams as well. PDX to Cascade locks. At White Pass, hitch east to Yakima and catch a puddle jumper to Seattle.
Another section I really enjoyed was from Dunsmuir / Castella up to Ashland. The climb out up into Castle Crags is quite nice, especially if you’re a rock climber - mmmm…granite. Etna was a great little town stop (one of my top 3 along with Wrightwood and Idyllwild), the Marbles kicked butt, the Russian Wilderness was quite nice, Siead Valley was an experience and it was just cool to finally get the heck out of California. It doesn’t compare with the JMT or North Cascades in scenery, but was a very nice few sections.
Token Civilian