Some other places:
Bend is cool. Great trails, outdoor focused community. Can be expensive, but you get what you pay for. Can feel a bit remote for an east coast person, but it would take a long time to exhaust the outdoor recreation opportunities.
Ashland is cool. Small college town, great parks, trail running community. Easy access to southern Oregon and northern Cali wilderness. Laid back. Southern Oregon has high unemployment, so jobs are scarce.
Corvallis is kind of nerdy/engineer with a bunch of flannel and chain saws thrown in for character. Some great ultra runners in the area. Thriving small college town. A bit underrated, but limited. One hour from Eugene, 90 minutes to Portland.
The coast is great for a visit, but not a great place for young people to live.
Salem is weird. Can't explain it, maybe because it is dominated by the state politics. I would not want to live there.
Visit Hood River (wind sports). Sisters (western themed town, spectacular views). Maupin (rafting), Crater Lake and/or Paulina. Get out to the Wallowas/Joseph near the Idaho border if possible.
Drive a loop from Eugene up Hwy 58 to the crest of the cascades, then take the Cascades Lakes Hwy back road to Bend. Drop a line in Crane Prairie Reservoir or one of the other lakes along the way if you like to fish for trout. Stop into downtown Bend for an evening. From Bend go through Sisters, then take the Old MacKenzie Pass as you head east. Stop at the Dee Wright Observatory made out of lava rock, surrounded by miles of lava flow. Plan a hike of the trailheads into the PCT or other wilderness trails in the area. Take a swim at Belknap Hot Springs or get directions to Cougar Reservoir. Continue on down the MacKenzie Highway back to Springfield, then Eugene, but stop and get out along the way when you can to admire the clarity of the river.
Stop at the Forest Service stations and browse. Talk to the Rangers on duty.
(Beware care break ins (clouting) anywhere along the way at trailheads.)
The U of O running club is very good and coached by Tom Heinonen, but I don't know if they are active in the summer. The only Portland club I know of is the Red Lizards.
The good weather usually starts in June, becomes awesome from July 4 until October. Try to get on as a last minute replacement for Cascades Lakes Relay in late July if you like relays with spectacular scenery.
Check craigslist for jobs. It is highly used in these parts by employers.
Sublet rent is cheap in the summer in the college towns. Eugene's semester starts back up in late September and the market tightens up then.
I moved out from the Midwest after college a couple of decades ago; left a good job for Oregon with no prospects and only $400 in my pocket, and never went back.
That should get you started. One thing you'll learn is that the state is smeared thin with attractions and you'll have the best time if you have gas money and reliable transportation.