You could cross at Sault St Marie and taking Hwy 2 across the country to Glacier National Park then drop down south to Yellowstone (include Grand Teton Nat'l Park next door). It's a very easy, pleasant drive. We always try to avoid interstates. One place you must stop in eastern Montana along Hwy 2 is Fort Peck Corp of Engineers campground. It's an oasis of huge sites and lawns. It's a nice resting place for a night or two.
If you want to see Grand Canyon then you'll drive through Utah and there are some more awesome national parks in southern Utah - Arches/Canyonlands, Capitol Reef, Bryce, Zion and also Monument Valley which isn't a national park but it's up there in scenery. Then head to Grand Canyon.
This is a very long trip. I hope you have a lot of time to make it worthwhile. You really could spend all summer doing this.
Moab, Utah (at Arches Nat'l Park) has an awesome biking trail and also extreme mountain biking the slickrock hills - lot of trails of all abilities. I'm sure if you Googled bike trails around the towns you'd be, you would find lots of opportunities for biking. I wouldn't recommend biking the paved roads in Yellowstone as the park is much too busy with narrow roads and lots of critters around to chase you.
🙂 Grand Teton Nat'l Park also has a nice bike trail along the main road with great views of the mountains.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel