Hi Jefferson,
Welcome! if you've got a car, a great and inexpensive place to start hunting for trout with a tenkara would be shenandoah national park (if you have a car or a fishing buddy with one). basically, get a map of the middle section of the park (Appalachian Trail map #10 is the best one i think), pick a blue line, and go - most streams have a trail running alongside them. A good place to the start would be the bottom of the rapidan by wolftown and work your way up the trail - you might have to scramble a bit. However, the brook trout there are native, and about to spawn, so I would check the fishing report from Murray's or elsewhere before you go to be sure you're not disturbing them. there are some stocked streams elsewhere with rainbows - check the maryland and virginia departments of game/inland fisheries for stocking schedules and locations. Anytime from March to May is pretty much going to be your go-to time for native trout, with stocked streams dependent on each state's stocking schedule.
As for an 8wt, that's pretty much the perfect size for the tidal basin. with the warmer weather recently, i bet the fishing is great over there. And you don't have to just target stripers - there are largemouth, cats, snakehead, and i think (?) there might even be smallies a bit upriver by chain bridge. We're really lucky with all the species we've got here in the area. Just swing a wooly bugger, clouser minnow, damsel nymph, or deceiver that's appropriate for an 8wt line and you'll likely hook up with something. You can even fish the tidal basin right off the monuments with a DC license - you won't get that experience anywhere else. Check out anything by lefty kreh on fly fishing for warmwater species. He loved fishing for bass on the fly and wrote a ton about it.
Does your 8wt have a shooting head on it (you mentioned salmon and alaska), or are you using weight forward floating line? WFF or sink tip will probably be the best for the water around here, if you've got it.
In March/April is the shad run. If you're familiar with salmon, it's kind of the same thing - american and hickory shad are andromous, and in spring they come back up the potomac and rappahannock to spawn. It's the big fishing event in DC, and your 8wt will work perfectly. Shad darts are really simple flies also, and i hear they are easy to tie if you tie.
Best of luck and have a blast.