What do you mean by "Western influence?" You mean in terms of culture?
Yes, and to a lesser extent, topography.
Hope this helps a little.
http://en.wikipedia.org/wiki/West_River_(South_Dakota)
It's about South Dakota, but some of it can apply to the other states as well (though not to the same extent, since North Dakota is historically more firmly linked to Minnesota. ND's policies are traditionally more communitarian, with its state bank).
West SD is very individualistic ranch country. MN, ND, to an extent East SD are more communitarian, in large part due to the Scandinavian, German, and some New England influence that's shaped the Upper Midwest culture.
West of the Missouri River in SD, it's traditionally mining country, and it's much more economically and culturally linked to Denver than to Minneapolis (lots of Denver Bronco fans in Rapid City; not so much in Sioux Falls). Politics in West River are more conservative than here in the East, but also more libertarian (West River rejected an abortion ban on the ballot even more strongly than East River).
Anyway, even the landscape West River is more rugged and dry than here in the cornbelt.
Kansas & Nebraska also have some of the Western cowboy heritage, even if they're also mostly Midwestern.