U.S. across Wyoming
Not really sure how Wyoming is in the Southwest but ok...
So, I'll be driving U.S. 20 from East to West.
Looking for places within a max of a half-hour or so of U.S. Route 20.
I'm interested in chicken, sandwiches, BBQ, ice cream parlours, etc.
No interest in Mexican or Seafood
I live a couple of hours from the Wyo border and I'm not sure either. Thermopolis is a cool town w/; a find private dinosaur museum, sensational natural hot springs and its own bison herd -- but no much in the way of terrific food. Expect a lot of burgers and steaks. The favorite Mex-ish place is/was Las Fuentes (sorry). There is/was an iconic ice cream stop in Shoshoni, which otherwise is pretty much a ghost town. It might be the Yellowstone Drug Store, or maybe not -- but its just south of where the highway makes a right angle turn. By Wyoming standards, Casper is a pretty big city. It also has lots of steaks, burgers, Tex-Mex (sorry), BBQ. Glenrock, about 1/2 an hour east of Casper, has/had a place called the Paisley Shawl that was pretty well thought-of.
I just noticed you're going east to west. Cody, where I've never been. There should be some fairly good places because of the Buffalo Bill Historical Center and its proximity to Yellowstone Natl Park.
In Cody ...
Rib & Chop House (as mentioned by another poster) is still fine, but not exceptional. Service can be spotty, especially in the summer, when the servers are prettier than they are efficient (male or female).
Sorry Mexican isn't for you because my current favorite is Tacos el Taconazado (sp?). Obviously Mexican, supposedly owned and run by a real Mexican family, it's been reliable, good, priced well, and unpretentious! Especially good tamales! (Perhaps someone else will find this helpful.)
In Powell ...
The Lamplighter is completely old-fashioned (tomato juice as an appetizer), but the meats are terrific! My first time there, I asked for a steak knife and was told that they didn't have them - if I couldn't cut my steak with the table knife, they'd bring me a different steak!
We had an excellent dinner at Wyoming Rib & Chop House in Cody (about 2 years ago, so take that into account). I had a fine ribeye, cooked perfectly medium rare, and my wife's ribs were fine. The place was crowded, so we appreciated the reservation our motel host - who recommended it - had placed for us (this was in July). Service was friendly, setting is casual, prices were very reasonable :) . It's apparently part of a local chain with a few locations in Wyoming and Montana; I can't speak for their other spots, but this one was fine.
We were traveling from Omaha to Glacier (going north to Sioux Falls, due west to Yellowstone, north to Bozeman and then on to Glacier), and this was one of the top meals on the trip. Other spots we particularly enjoyed along the way were Chef Louie's in Mitchell, SD; Deadwood Social Club in Deadwood, SD; The Virginian in Buffalo, WY (outstanding); dinner at the Yellowstone Lake Hotel; and breakfast & dinner at the Izaak Walton Inn in Essex, MT.
Kabocha - Since this post, Wyoming joins Colorado and others in s Mountain States section of Chowhound -- where we belong.
Having written that, I was recently in Cody. Rib & Chop House was OK, but the Terrace outside of town was better, Avoid the Hotel Irma. The vegetable du jour was limp overcooked green beens with cold bacon bits and small dices of something red (tasteless red peppers? tasteless tomatoes?). The rest of the dinner fare match. If you must go there, breafast is a better bet.