You should get on # 20 when you get to Wyoming if you get bored of the Interstate 90. There's some fun places to stop there. Go on W to Idaho if you get a chance. That's pretty country. Here's a few road stops for you.
When you get to Thermopolis, WY stop at Lil Wrangler Restaurant and Drive In on Highway 20 for good breakfast, lunch or dinner. Go E on Broadway in Thermopolis, WY to Prospector for good Italian pasta and pizza or Pumpernick's for good country good and outdoor dining. Stop at Butch's Place in Kirby, WY just N of Thermopolis, WY for good steaks and cold drinks. Stop in Worland, WY at Ranchita Cafe on Big Horn Avenue for outstanding Mexican food for lunch or dinner. If I were crossing WY on Highway 20 I would plan a side trip on Scenic Highway 14 through Big Horn National Forest and the Big Horn Mountains. I would spend a night at Bear Lodge Resort and dine at Moose Crossing Restaurant at the lodge. Your side trip to Scenic Highway 14 could originate in Greybull. Stop in Greybull for the night and dine at Lisa's. I would spend the night at The Historic Greybull Hotel on Highway 20. You could walk to Lisa's down the street 4 blocks. Stop at Granny's Restaurant in Cody, WY for outstanding country food for breakfast, lunch or dinner on Highway 20. Zapata's on Highway 20 in Cody, WY has good Mexican cuisine. Wyoming Rib and Chop House is a nice restaurant for good steaks and seafood. Proud Cut Saloon has good burgers and sandwiches for lunch and dinner. Fill up your gas tank and drink some cold water. It's 3 hours to your next stop in West Yellowstone, MT. Take a left on Madison Ave. in West Yellowstone, MT and go to Trapper's Family Restaurant for good country food for breakfast, lunch or dinner. There's a nice view of the Teton's. Take a right on Madison Ave. and go to Bullwinkle's Saloon and Eatery for outstanding burgers, sandwiches, BBQ ribs, steaks and seafood for lunch or dinner. Go to Running Bear Pancake House for outstanding breakfast or lunch on Madison Ave. Stop by Mack's Inn Resort for the night and have breakfast, lunch or dinner at Henry's Fork Landing Restaurant. Stop by Trout Hunter on Henry's Fork for the night and have breakfast, lunch or dinner at their Last Chance Bar and Grill. Stop by Stockman's Restaurant for a nice lunch or dinner in Rigby, ID. Take Lindsay Blvd. in Idaho Falls, ID and go S to W Broadway. Take a left and go to Smitty's Pancake and Steak House for outstanding breakfast, lunch or dinner. For fine dining for lunch or dinner in Idaho Falls, ID take a left off Broadway on River Parkway and go to Rutabagers. Brownstone Restaurant is a fun place for lunch and dinner just up the street from Rutabagers on River Parkway. Stop at Grinde's Diner in Mountain Home, ID for fine breakfast, lunch or dinner.
Lil Wrangler @ 800 Shoshoni Street, Thermopolis, WY 307 - 864 - 4180
Prospector @ 500 Broadway Street, Thermopolis, WY 307 - 864 - 3343.
Pumpernick's Family Restaurant @ 512 Broadway Street, Thermopolis, WY 307 - 864 - 5151. http://pumpernicksfamilyrestaurant.com/
Butch's Place @ 101 East Main Street, Kirby, WY 307 - 864 - 2669.
Ranchito Cafe @ 544 Big Horn Avenue, Worland, WY 307 - 347 - 8501.
Bear Lodge Resort @ 5600 US14A, Dayton, WY 307 - 752 - 2444. http://www.bearlodgeresort.com/
Lisa's @ 200 Greybull Avenue, Greybull, WY 307 - 765 - 4765. H20. http://www.lisaswesterncuisine.com
Historic Hotel Greybull @ 602 Greybull Avenue, Greybull, WY 307 - 202 - 0329. http://historichotelgreybull.com/
Granny's Restaurant @ 1550 Sheridan Avenue, Cody, WY 307 - 587 - 4829.
Zapata's @ 1362 Sheridan Avenue, Cody, WY 307 - 527 - 7181.
Wyoming Rib and Chop House @ 1367 Sheridan Avenue, Cody, WY 307 - 527 - 7731. http://www.ribandchophouse.com/
Proud Cut Saloon @ 1227 Sheridan Avenue, Cody, WY 307 - 527 - 6905.
Trapper's Family Restaurant @ 301 Madison Avenue, West Yellowstone, MT 406 - 646 - 9375.
Bullwinkle's Saloon and Eatery @ 19 Madison Avenue, West Yellowstone, MT 406 - 646 - 7974. http://www.yellowstonebullwinkles.com/
Running Bear Pancake House @ 538 Madison Avenue, West Yellowstone, MT 406 - 646 - 7703.
Mack's Inn @ 4292 Highway 20, Macks Inn, ID 208 - 558 - 7272. http://www.macksinn.com/
Trout Hunter on the Henry's Fork Lodge @ 3327 N Highway 20, Island Park, ID 208 - 558 - 9900.
The Last Chance Bar and Grill @ 3327 U.S. 20, Island Park, ID 208 - 558 - 0919. http://www.trouthunt.com/
Stockman's Restaurant @ 3 North 3800 East, Rigby, ID 208 - 552 - 6500. http://www.stockmansrestaurant.com/
Smitty's Pancake and Steakhouse @ 645 West Broadway Street, Idaho Falls, ID 208 - 523 - 6450.
Rutabaga's @ 415 River Parkway, Idaho Falls, ID 208 - 529 - 3990. http://www.rutabagasidahofalls.com/
Brownstone Restaurant and Brewhouse @ 455 River Parkway, Idaho Falls, ID 208 - 535 - 0310. http://brownstonebrewpub....stone_Brewing_Co..html
Grinde's Diner @ 550 West 6th South, Mountain Home, ID 208 - 587 - 5611. http://www.grindesdiner.com/