State Forests!
You can shoot in any state forest, so long as you follow this:
http://arcweb.sos.state.or.us/rules/0405_Bulletin/0405_ch629_bulletin.html
Feel Free to wear your weapon on you, but be polite if the authorities ask you to unload it in their presence.
There have been several shootings in memory of folks out for a good time with their guns. Larch Mountain is the most recent big one--two hunters killed while sighting in their rifles before hunting season. For this reason, the buddy system isn't a bad idea.
The authorities will sometimes stop in and say hi, occasionally asking you to put the weapon in the car or unload it. (never happened to ME, but it did happen to a friend). Don't be offended, they are only there to say howdy and show the flag. Heck, some them also discuss guns with me, comparing sidearms.
Oh, and bring bug repellent. When I was out two weeks ago, I was eaten alive.
Now, as to WHERE: about an hour out of Portland you will find the Tillmook and Clatstop State Forests. Go west on HWY 26 and keep going on 26, you will pass through a finger of Tillamook, then just into Clatsop, you will find a BUNCH of logging roads. I am fond of Section 10 road, personally, but as long as it isn't marked "private drive" you are good to go. Verify BEHIND your target and any ricochet trajectories. Look for families having picnics and hippies hugging trees, and shoot away.
Use your head, be polite (and friendly--wave!), and law abiding and have a GREAT time.