Tillamook State Forrest is great for some actual off roading. Go across the river for a day trip of back roads and fun puddles and some hills into the forest above Washougal. Follow the Barlow Trail Road over Mt. Hood. Or if you want more overlanding type of material, head over the mountains to the east to the hundreds of miles of open dirt roads in the desert.
For where to take your Rover for the doctor, visit Ship's Mechanical near the airport, or Columbia Roving downtown.
Almost 2/3 of Oregon is desert: https://flic.kr/s/aHsjvJTUXJ