US2 all the way from Duluth to Sandpoint Id makes a lot of sense. It's kind of flat and boring across the plains, but that's true of all the roads in that area. I94 to the south passes through Teddy Roosevelt NP, and I90 further south passes by the Black Hills.
US2 gives good access to Glacier NP, both east and west sides.
Across Washington you have several options.
Spokane is the largest city on US2 after Duluth. West from there it crosses flat wheat country, then drops down to the Columbia River. A side trip here is north to Grand Coulee Dam. There are various camping and boating options along the Columbia River and the lakes its dams have formed.
Then US2 climbs gradually to Stevens Pass, and then down to the Seattle area. It gets busy in the Sultan Gold Bar Monroe area, and then into Everett.
To go on to Neah Bay you could take the ferry to Whidbey Island, and then another to Port Townsend. The rest of the way to lands end is US101 and then lesser state highways along the coast. And check out the options that the Olympic NP offers.
An alternative to US2 across washington is WA20. You could switch over to that at several points. You could catch it in the east at Newport. Or you could continue NW from Grand Coulee Dam, or catch state hwys from US97.
The most scenic part of WA20 is Winthrop west over Washington Pass, through North Cascade NP.
At the Sound WA20 crosses river delta country and then on to Whidbey Island at Deceiption Pass (a popular State Park).
Some might recommend skipping the ferries and going south around Tacoma and Olympia. But that's a lot of city driving. To really bypass the cities and ferries, you need to take US12 across southern Washington. You could pick that up in Montana, south of Missoula. US12 puts you closer to Mt Rainier. From the west end of US12 you could take US101 around the west side of the Olympics.
In fact I'd recommend staying north, US2 or 20 going one direction, and returning further south (or north into Canada).