He was born in Texas, won his first term as resident of NY, his second term as resident of PA, but Wiki, the History Channel presidents documentary and other sources list his home state as Kansas. So which one should it be?
Usually the state of residence at time of an election is being considered a "home state". However, that can be tricky. Nixon for example won his first term while residing in New York, and the second while in California. California is considered to be his "home state" because he was born and grew up there, was elected to the House, Senate and Vice Presidency from there and returned there as President.
Ike grew up in Kansas, so that's probably why. Of course, after joining the army he didn't have a "home state" in political sense, being transferred from one assignment to another.
Due to his lack of a political past (and political base) he can't be easily classified like the other Presidents.