Yellowstone is a two day drive each way, and is WELL worth the visit.
Most of the park will be open by early June, although a few roads in the high country may still be closed due to lingering snow.
for an idea of what to expect. Assuming you've never seen the geothermal features or the region's abundant wildlife, you could easily spend a half a week there, just shooting the major "typical tourist" sights. There will be plenty of places to camp. If staying in a motel, I'd suggest Cody or Gardiner over West Yellowstone (a real tourist trap, IMO.)
After that, head south to Teton National Park. It's smaller, but offers rewarding hikes into the mountains, leading to gorgeous alpine lakes.
Along the way, you could visit northern Michigan. There are several parks in the area that are smaller, but roughly comparable to the Algonquin area. Sorry, I'm not very knowledgeable about the area. Hopefully your friend can offer better advice.
On the way to Yellowstone, etc., there are a number of grassland preserves in North and South Dakota that you might enjoy stopping / camping at. If nothing else, they will offer your eyes a break from mile after mile after mile of corn! Eastern Wyoming has several pretty areas and a few parks, such as Devil's (Bear's) Tower. Highway #212, running between Billings Montana and the northern Yellowstone area is a great drive. Check to see if the road is open visiting the area. Beyond that, you could head north to Glacier National Park, then cross into Canada to visit Banff, Jasper, etc. in the equally pretty Canadian Rockies. Check to see when these parks open for the season. Glacier is somewhat similar to the Canadian parks, and you might not want/need to visit them all.
The highly photogenic red-rocks of Southern Utah are only a day's drive from Yellowstone. Depending on how much time you plan to spend on the road, you could easily visit a few of the parks in the area. Bryce, Arches, Canyonlands, Capitol Reef, the Escalante area, or even Zion (the furthest) are all within a half day's drive of one another. That's not to say you should try to hit them all! Be sure to slow down, get out of the car, and ENJOY the areas you're visiting! I'm fairly familiar with the Utah region; PM me if you have specific questions or are looking for more details and destinations in the area. http://maps.google.com
is a good on-line resource for basic trip planning. Enable 'photos' to see pictures of the areas you're considering.