In which U.S. state is it easiest to obtain a state banking license?

Generally if you're not looking at California, Texas or New York, you relatively have a much easier task at hand. Each's state's licensing methodology varies, but it will inherently be a lot simpler and easier than CA, TX and NY (collectively know as the 3 hard states to crack).

Your other option is to look at local state based community banks up for sale.