Today the Census Bureau released County-to-County flow data based on the 2007-2011 ACS. This year the flows are cross-tabulated with education and income (individual and household). Last year they were cross-tabulated with sex, age, race and Hispanic origin.
More on that release HERE and HERE.
Data can be found through HERE and they have a mapping application where you can find out where people with certain characteristics come from and go to.
See also the data tabular format on a new web page. You can find estimates of the characteristics of people moving in and out of each County (“Overview”) or you can get estimates of the characteristics of people moving between two New York counties.