Dang, Big Ben. I'm impressed that you even remembered that.
I have taken many bicycle tours in the US over the past 40 years. The duration of the various rides has ranged from 2 days to two months. Over 95% of my riding was done on asphalt roads with tent camping each night. In general, I think that "bikepacking" involves much more off-road riding, with some asphalt roadways included. But I'm not exactly sure where the line is drawn.
The Oregon Coast is a beautiful route if you don't mind a bit of automobile traffic alongside you while you ride. I've done it twice. Riding north to south along the coast for nominally 350 miles from Astoria to Brookings, you are able to remain on the side of the road closest to the Pacific Ocean to improve your daily views. IIRC, for all but one stretch near Brookings, there was a State Park roughly every 40 miles or less. Camping fees when I went a few years ago were just $4.00/night per cyclist. Mid-summer temperatures were crazy-comfortable for a old guy used to the Texas heat.
There's a pretty nice route crossing the borders of Idaho, Washington, and British Columbia (Canada). It is called the Selkirk Loop. Nominally 300 miles over asphalt roads, campsites are available every 25-50 miles along the way. The ride includes riverside roads, lake camping, and a 5-6 mile ferry ride across Kootenay Lake.
If gravel is more your thing, there is a Rails-to-Trails route connecting Kansas City and St. Louis, Missouri. It is the seamless combination of The Katy Trail and the Rock Island Trail. Nominally 300 miles of cycling on a relatively firm crushed rock trail, this ride is relatively flat -- it's an old railroad route. There are small town stops along the way and tent camping available every night. My daughter and I made a real baseball themed trip one year -- dubbed The Doubleplay Tour -- taking in the Cardinals season opener in St. Louis and the Royals home opener in Kansas City. We even slept at a little league baseball field one night!
Ragoo talked about the Blue Ridge Parkway. Camping spots are far between on that road. But a fair substitute is the Natchez Trace. Connecting Natchez, Mississippi, to Nashville, Tennessee, this well maintained road has fairly low automobile traffic. I've ridden only the section from Jackson to Nashville. But I was impressed with the pleasantness of the route and the friendliness of the people. Campsites include State Parks, city parks, and even a spot in the back yard of a fire station.