After the Grand Tetons, find your way to Idaho Falls and follow hwy 20/26 across Idaho. Make sure to stop at the Craters of the Moon Monument.
It looks like you picked hwy 20 across Oregon. You might want to consider hwy 26, it is a little more scenic. Take 26 to Prineville and then 126 west through Redmond and into Sisters (a nice little town). From Sisters take the Old McKenzie Highway (hwy 242) across the cascades stopping at the Dee Wright Observatory. Follow 242 down to 126 and then turn around and come back across 242 (trust me, it is worth it, especially if you can drive it on a weekday.
Back to Sisters, take 20 south to Bend and find your way to SW Century Drive, it turns into the Cascades Lakes National Scenic Byway. From there take a short hop down hwy 97 to hwy 138 that will take you to Crater Lake.
If you have an extra day, I recommend driving down I-5 into California and crossing to the coast on hwy 96. This is a great highway and puts you into the heart of the redwoods.
Depending on how far you want to make it up the Oregon coast, I recommend taking hwy 53 from Wheeler to hwy 26 (lunch at Camp 18?), then hwy 103 north to Jewel, then hwy 202 to Mist, then hwy 47 north to Clatskanie and hwy 30.
Hwy 30 will take you along the Columbia River to Portland and hwy 84 through the George.