[font color=\'#000000\']"Eastern Oregon" is pretty general. That's a BIG area, and that area contains some of the most remote desert areas in North America.
In the extreme north east, the Blue Mountains, specifically the Eagle Cap Wilderness and Hells Canyon Wilderness areas are very challenging. Good asphalt routes here are OR 82 from La Grande to Enterprise and OR 03 north into WA.
Most of the northern slice, south of the Columbia from The Dalles to Pendleton is rolling, high-elevation farmland, nice country and great roads.
Immediately south of the farming corridor is John Day country, centered on John Day (US 395 US 25) is very pretty country, offering ranch lands, bentonite hills (very colourful) and lovely river valleys. Any highway in a 100 mile radius centered on John Day will please.
The south center has wide open, relatively flat desert terrain, with the exception of the Albert Rim, north of Lakeview on US 395. This piece of geography can be just plain amazing in the right light.
OR 140 from Lakeview to Denio, connecting back north via OR 292 and OR 205 along the Catlow Rim is spectacular remote desert mountain country and excellent for landscape shooting. I love these roads. The Alvord desert, immediately to the east of OR 205 is a favourite car commercial location, somewhat similar to the Black Rock Desert in NV.
The Maleur NWR south of Burns teems with life, depending on the time of year. I'd consult with the NWS for info on this.
The US 97 corridor from Bend southward to NV is, for me at least, dead boring. I always try and do this stretch at midday or at night so I'm not missing any good light. If you need southward movement, try OR 31 via Silver Lake, Paisley, Lakeview.
It really doesn't qualify as "eastern", but Crater Lake is one of the continent's least-known, highest-value treasures. It rates a 10 in my book in all respects save accommodation and food.