Indianapolis has a Democrat Mayor, but he is not to be confused with, say, the mayor of Baltimore. The overwhelming majority of cities, and the counties they are in are as you describe. However, Indiana is entirely red for congress except for the two districts that include Indianapolis and Gary (go figure). Indiana has one Repub senator and one Dem. The Governor is a Republican. The policies of IN are conservative for the most part.
You may want to do more research before offering up incorrect statements.