There are several ranges around Oregon.
I am from the Portland area. I know of:
The Place To Shoot: http://www.theplacetoshoot.com/TPTS/Welcome.html
North Portland in Delta Park.
Beavercreek Armory: http://www.beavercreekarmory.com/
Hillsboro, just off Hwy 26th and NW Helvetia Rd.
Tri-County Gun Club: http://www.tcgc.org/
Between Sherwood, OR and Tualitan, OR
Johnson Creek Gun Club: http://www.johnsoncreekgunclub.com/
Near Johnson Creek Blvd and 82nd Ave in Clackamas, OR
You can also go East towards the Cascade Mountains or West towards the Coast Range. A document with some rules is here: http://www.oregon.gov/odf/tillamookstateforest/docs/TargetShooting_OARs.pdf
If you are on BLM lands they too have some rules. You would need to look up on the internet the are you are going.
I have gone west from Portland on hwy 6 to Tillamook turning south near mile post 27. And sometimes west out hwy 26 to Seaside turning soouth near mile post 30.
Hope this helps!