There are a couple of motels in Wright, but I cannot vouch for the quality. Otherwise, your options are Gillette, about 40 miles north, Douglas, 75 miles south, or Newcastle about 75 miles east of Wright. Newcastle is on the edge of the Black Hills and in traveling distance of Lead and Deadwood in South Dakota if you're into gambling. Nice scenery if you're not. Understand that Wright is in pronghorn country which means flat, dry, and not very "scenic." More so this year because the whole state is in a severe drought. The only thing worth seeing between Wright and Gillette are the massive open pit coal mines. Just saying that unless your wife is hunting with you, there is not much to do in Wright to keep her entertained. Gillette is an energy boom town. Whereever you plan to stay, make reservations well in advance. Not only lots of hunters in the season, but also drilling and construction crews in abundance. There was a nice motel in Newcastle called The Pines, located in a secluded shady area and reasonable rates. However, I haven't been there in a couple of years and it may have changed hands. Douglas is on the North Platte River and has public fishing access.
Good luck on your trip to my state. You will find it quite different from your home state. Ask more questions if you like, I will try to help.