Mcdonald's, Burger King, Wataburger... Those represent Oklahoma "in general" (as well as most of the country) I'm guessing you really want something better than that though.
Well, if we are going down that route, definitely Braum's Ice Cream Stores. Their dairy and factory are all in Oklahoma.
And, if old firearms and military hardware are of interest to a new guy, check out the 45th Infantry Museum in Oklahoma City near NE 36th and Martin Luther King Blvd.
Link to my photos of the 45th Infantry Museum: 45th Infantry Museum