hey Pho, i just moved here last year, been slowly figuring out my favorite places the last 6 months or so, figured i'd throw what i've learned so far.
one of my favorite trout lakes is Lake Harriet. it's a bit of a drive from Beaverton, about 1.5hr, but it has decent bank access along a floating dock at the east end, and a few good bank access spots all along the north side down to the dam. if you have a small watercraft, you can really get to some great water near the dam and along the south shoreline. great trout lake, stocked with rainbows and has native browns. might be a little slow with the heat this time of year, but it should pick back up once it starts to cool down a bit here in a month or two. it's also just super pretty and peaceful there, so even if you don't catch anything, you'll still have a nice day in the Mt. Hood wilderness. Bonus: if you're into camping, there's TONS of undeveloped (no fee) campsites all around that area within a few minutes drive of the lake if you wanted to make a weekend or more of it.
more generally, if you like trout fishing in lakes and are up for a bit of a hike, there's TONS of hike-in lakes in the Mt. Hood area that are usually within a 1-3 mile moderate hike, and almost all of them have some sort of trout, whether it's native browns, cutthroats, or bulls (always release bulls), or stocked rainbows/browns.
Hagg lake is nice too, but i've always felt like i'd do better there with some sort of watercraft to access some deeper water. i had some good luck fishing for trout there this spring, and caught a few smallmouth and one largemouth back in June. there's also bullhead cats in there if you're into catfish, but i've never bothered. there's decent bank access to deep water near the dam and a few other spots, but Hagg is pretty big. i'd love to have a boat so i could get to some of that deeper water in the middle.
trolling seems to be really popular around here, nearly every lake i've been to has had a gaggle of boaters trolling around. makes me jealous for not having a boat
as far a rivers go, the Wilson will be the closest from Beaverton/Hillsboro, only about a 1/1.5 hr drive. there's TONS of bank access along the Wilson as rt 6 follows the the river from Elk Creek into the tidewater at Tillamook. Just look for the pull-outs along the road and follow the trails if you can't see the river from the pull-out. I've been on the Wilson a few times this summer trying to land my first steelhead with no luck (yet!). Cutthroat trout are also in the Wilson, and are pretty easy to catch once you find them. Biggest problem with fishing the Wilson in the summer (and especially right now) is the swimmers. not that i have a problem with them, but the fish do, so get there super early (sunrise) or go right before sundown once the swimmers have left for the day. swimming pressure should ease off in the next month or two as well.
i'd suggest spending a little while on google maps with sat. view to scout rt. 6 for pull-outs along the Wilson before you go. some of those pull-outs will sneak up on you if you're just cruisin' by, and some people like to drive fast on that road, so just be careful pulling in/out from the road. Good Luck!