For a real thrill, a survivable adventure, get off I-5 northbound past Weed at Edgebrook and take the westside road north to Gazelle, then west to Callahan, Cecilville, and Forks of Salmon, the CA-3 junction. Take CA-3 NE to Yreka; or continue W on CA-3 to Soames Bar, the CA-96 junction, and follow CA-96 NE along the Klamath River past Happy Camp and Scott's Bar back to I-5 N of Yreka. All these roads are paved, more or less. The Cecilville road, Forest Hwy 93, can be rather exciting.
Lava Beds NM, SE of Klamath Falls. Fantastic place; learn about the Modoc War.
The drive around Upper Klamath Lake and Agency Lake. Note the superb views of Mt McLaughlin, Oregon's Mt Fuji. That drive convinced us to buy land in Chiloquin. (We've since sold it.)
Collier Mem. State Park, just north of Chiloquin, SE of Crater Lake -- logging museum and pioneer village. Now, this isn't spectacular by itself. But just south of the park is a small bridge where Hwy 97 crosses what's called Spring Creek. Nice place to fish, under that bridge. And a couple miles further north is FS Road 9732 (I think that's the number) going NW to the Spring Creek Rec Site. Follow that road around to the end. You have now reached one of the most mystical places I know, morning and evening. Spring Creek is only about 1/2 mile long. It bubbles-up here, like a leak from the bottom of Crater Lake (just a few miles NW). The water and air and light are magickal. I love it there.
While visiting Ashland, go a little ways NW to historic Jacksonville. For a beautiful drive, go W from Jacksonville on OR-238 along the Applegate River to Grant's Pass, then return E on Rogue River Hwy (S side on the river; I-5 is on the N side). Wave at my cousins as you pass Gold Hill -- and skip the "Mystery Spot" there, it's a rip.
I could point out lotsa other good stuff in the Great State of Jefferson (Crater Lake; Newberry Volcano; Rogue River Jet Boat; Weaverville CA, Castle Crags SP) but this will get you started. Have fun!