Via Matt Yglesias, this map at Slate shows how how population changed at the county level during the Depression. Counties in the wheat area/Great Plains suffered a loss of more than 10 percent during the 10 years, in some cases more than 25 percent. That's not just the children growing up and moving away, that's families moving (i.e., Steinbeck's Joads and the other Okies.).
The distress behind those population changes is why the New Deal passed a bunch of laws relating to agriculture and rural life.
A note: as I blogged yesterday the 1940 census records included a question on where you lived in 1935, so it should be possible to construct a map showing migration during 1930-35, and 1935-40.