E Yellowstone to NY

While the suggestions posted are good, I'd take a different route completely -- I-90 across South Dakota to I-25 at Sioux Falls, then south to I-680/I-80.

Hwy 14 over the Bighorns at Greybull or Hwy 16 over them at Worland would both work, but 16 is a little easier and just as scenic, imho. This would lead you to the historic town of Buffalo (Johnson County Range Wars), where you'd pick up I-90.

From there I'd suggest a slight excursion at Moorcroft to visit the nation's first National Monument, Devils Tower, then head to Sundance (namesake of the Sundance Kid) and I-90 again. This will place you at the edge of the Black Hills, where you'd have any number of interesting sites to explore including Mt Rushmore, Crazy Horse Monument and Custer State Park, to mention just a few.

Once leaving the Black Hills you'd be only an hour from the South Dakota Badlands, another great short excursion from the interstate (not to mention Wall Drug).

The rest area just past the Missouri River bridge at Chamberlain provides a very nice scenic view of the river and the rugged plains beyond it. East of the river is farm country; west of it is cowboy country, and it's so different that residents of the state identify as either "east river" or "west river".

Normally I'd recommend a quick stop at the Mitchell Corn Palace, but it's currently being renovated and has lost its charm for the summer. Mitchell does have a nice Cabellas, if you're so inclined, as does Rapid City.

If you take I-25 south at Sioux Falls, don't miss the I-680 exchange and stay on I-25. I-680 is a direct route to I-80 through some pretty country and will save you 40-50 miles (wild guess).

Try to stop at the first rest area when arriving in each state to gather tourist information. It'll make your trip through each state much more interesting and you'll be less apt to miss something that would appeal to you.

Good suggestions so far. Besides the hot springs in Thermopolis there is Legend Rock and the Dinosaur Museum. Fort Laramie is not far from US-26. If you are into Cabella's the one in Sidney even has a campground and there is another Cabella's in Kearney. Guernsey and Fort Kearney State Parks both have campgrounds. The Great Platte River Road Archway on I-80 is worth a stop.

The Amana Colonies are not too far North of I-80 and Winterset is not too far South of I-80 in Iowa.

If you need chrome, don't miss the I-80 truck stop just west of Davenport, IA. :)

Good summary by Cloud Driver. The route he describes includes US 26, going southeast by Guernsey SP and Scotts Bluff, Nebraska, connecting to I-80 around Ogallala, Nebraska, and I highly recommend it. Good road, not that many towns along the way to slow you down, and some interesting sights along the way. And yep, pretty much corn & soybeans along I-80 from at least Grand Island east. :) There are some neat pioneer-related sites in Nebraska, clustered around Kearney (Ft Kearny, previously mentioned, and the big arch across I-80 which includes a delightful museum about the westward movement) and Grand Island - York (Stuhr Museum of the Prairie Pioneer, for example).

(double post)

Not sure what your plan is to get to I80, but here are a few suggestions to relieve the boredom.

From Cody head south on route 120 for a soak in the hot spring pools. Then continue on route 20 through the Wind River Canyon to Shoshoni and on to Casper to pick up I25. Get off the Interstate onto route 26 to Guernsey to see the best preserved Oregon Trail ruts and Register Cliff with Pioneer names still visible in the rock. Nearby Guernsey State Park has electric hookups. Continue on route 26 to Fort Laramie with some restored buildings dating from the Oregon Trail days. Further down route 26 are Scotts Bluff, Chimney Rock, Ash Hollow and Windlass Hill, also Oregon Trail sites. At North Platte is the home of Buffalo Bill Cody and also the Bailey Yard of the Union Pacific RR. This yard was part of the original Transcontinental RR and has grown to be the largest RR yard in the world. The Golden Spike Tower (fee) provides an elevated view of the yard operations. At Kearney is Fort Kearney, also dating from the Oregon Trail days, but not much there compared to Fort Laramie.

Further east, it's pretty much corn and soybean fields all the way.