I love your question! Like you, I must have elevation hiking, and I live near Rogue River. My Adam Sawyer has written a book on waterfall hikes in Southern Oregon; he also wrote a Travel Oregon story about specific waterfall hikes along the Umpqua and Rogue River.
You can also go the other direction from Rogue River, and hike at elevation around Mt. Ashland and Pilot Rock. My favorite hike is along the Pacific Crest Trail, which can be accessed at the Siskiyou Pass just off I-5. At Callahan’s Lodge, go right toward Mt. Ashland and you’ll see the PCT signage. The PCT goes north toward Hyatt Lake (lower elevation), but south to the top of Mt. Ashland and over toward the CA border. It’s a beautiful hike, and along the way, you’ll see a ready made shelter for you just past the Mt. Ashland campground.
You can also hike Pilot Rock (also a side trail of the PCT), which you can access within about 30 minutes from Rogue River. Get directions here. While you will need to be free of a fear of heights to hike Pilot Rock, even those not wanting to accent to the top can enjoy the views at the base. I also like Grizzly Peak, which is nearby of Highway 66. Get directions here.