Camping on public lands in the West -
You can camp free on most public lands in the West - there are 3 major agencies - Bureau of Land Management (tan on maps), National Forest Service (green on maps) and National Park Service (sometimes purple, sometimes dark green). On BLM and NFS lands it is okay to camp anywhere 1 mile away from developed campsites. This doesn't apply for NPS lands. Also state lands (light blue on maps) usually have significant restrictions.
Coming across Lake Michigan will put you into Manitowoc - - check out the Wisconsin DOT website and find the bicycle program - - Wisconsin has incredible bike maps which show rural roads with very low traffic. You can download county maps from this webpage.
Minnesota - has some great east-west rail trails in the southern part of the state.
Cannon Valley and Saketah from Red Wind thru Northfield to Mankato.
South Dakota - I prefer crossing South Dakota because of the Black Hills - SD 34, US 14 yo SD 44 is a nice route across to Rapid City. The western Black Hills have wonderful meadows with brooks running thru - if you can do a few dirt roads. Also Mickelson Trail -
Wyoming - the best state for cycling - from Four COrners you can cut up to Sundance and then to Devil's Tower of "Close Encounters" fame. There's service road that parallels I-90 from Moorcroft to Gillette - coal mining/industrial. Don't get on I-90 west of Gillette like so many cyclists do - why are you biking anyway?? to smell diesel fumes??? Take 14/16 which is a great ride. Winds are usually southwesterly so do the stretch to Spotted Horse in the afternoon and maybe catch some tailwinds, make sure to do the stretch into Buffalo as early as possible so you don't have as much wind. The ride into Buffalo follows a creek with panoramic views of the Big Horns.
US 16 is the easiest route over the Bighorns - even if the pass is higher. The Bighorns have the most beautiful wildflowers in the West in late June/ early July. If you can get offroad, absolutely do Crazy Woman Canyon - head south of Buffalo on WY 196 and up Crazy Woman Road which reconnects with US 16 east of Powder River Pass. The ride down Ten Sleep Canyon is a jet plane. There are two hairpin curves marked well in advance - but after the second, you can let her rip. Most maps show the road from Ten Sleep to Manderson as unpaved - it's paved and very empty.
From Cody into Yellowstone you might want to consider Dead Indian Pass (WY120/296) rather than US 14/16/20. They are doing major work - you'll probably have to wait and then be shuttled - plus it's super ugly. Camp outside of the park near Silver City and hike into the wilderness area in Montana - superb and far less restricted than camping in the park.
Montana - Cutting thru southern Montana is much nicer than eastern Idaho. If you are on a mountain bike you can do part of the CD Trail thru the Centennial valley to Lima and cross the Bitterroots at Lemhi Pass to get to Salmon, Idaho. The paved option is the Adventure Cycling route to Lost Trail Pass then south on US 93 to Salmon.
Idaho - The Salmon River is a beautiful ride up to the Sawtooth Mountains at Stanley. The Rec Area is as beautiful as any national park with far fewer restrictions on cyclists. Follow ID 21 west along the Payette River - killer downhill - west of Lowman take the paved county road along the river - lots of natural hot springs where you can camp and soak.
Oregon - a very bike-friendly state - two major east-west routes - US 26 and US 20. US 26 is the Adventure Cycling route, is more scenic, and has more forest cover which may reduce headwinds. If you like the "remote" thing - then take US 20 - both have light traffic east of the Cascades. If you don't have to hit central Oregon - cut down to Crater lake and take OR 138 downhill along the Umqua River all the way to Roseburg.
Drop me a line if you have any specific questions.
Best - J
Pix - Ten Sleep Canyon, Hayden Valley, Salmon River, Sawtooths