EDIT - didn't see that you were looking just for rural land. Yes, there's lots of BLM land, but you're looking at a fairly good drive, 30-45 minutes at least from Eugene to find somewhere you won't be hassled, Eugene is getting pretty built up. And don't forget, it's Oregon, not San Diego, it rains 8 months a year. I think you'll find that a range with a roof over your head can be very pleasant much of the year.
Depending on exactly where you move I'll invite you to my range. It's 25 miles north of Eugene, but it's right off I-5 so it's easier than driving back roads, and it's a great facility. It's the Albany Rifle and Pistol Club,
www.arpc.info, located just north of Brownsville, where I live. If you end up on the north side of Eugene or Springfield it will probably be closer than anything else. My daughter lives in Eugene and she comes back here all the time to shoot because she can't find anything nearly as nice within a decent drive.
The club owns about 40 acres of land around a butte, with the main (rifle) range on the west side and pistol bays on the north. All are covered, the pistol bays are set up as 7 minuature individual ranges, soon to be 12.
There's IPSC, Cowboy Action Shooting, 3-gun, bowling pins, Hipower, benchrest, blackpowder, full-auto and lots of other events always going on. Good attitude, very few rules, which boil down to "be safe and have fun", no "range Nazis" to be found.
Cost is about $75 per year for card lock access any time, and they ask for 12 hours of volunteerism during the year or pay another $75. If you have any questions give me a PM.
Eugene has some indoor ranges, I know of "The Baron's Den", and there is the Isaac Walton gun club there, which is an outdoor range I believe, a Google search on those should give you some info.