A few miles north from La Grande on I84 is a forest road (NF21) at exit 248. Turn left at bottom of ramp, and about 2-3 miles is a free Nat Forest CG, Spring Creek. https://www.fs.usda.gov/recarea/wallowa-whitman/recarea/?recid=52121 Not big, but should be ok for your rig.
OR, keep heading into the woods, and along NF21 you'll find quite a few dispersed sites. If you use google maps or google earth, you can see a lot of them. A couple are on the free campsites site mentioned previously. Some could be muddy if early June, and on the weekends, you'll run into a fair amount of ATV's running around!!