I'm re-reading The Grapes of Wrath, and since I know how bad things turn out for the Joads when they head to California, I was wondering where they should have gone instead.
First some major points, the Joads were farmers/unskilled workers. These employment groups were hit hardest by the depressions as the industries that used them cut production while farming which had never enjoyed the boom of the 1920's collapsed. There were little employment opportunities for such people in most of the country, many went to California as it was the last main agricultural area left after the Dust Bowl destroyed prairies.
As for places not hit by the depression there were few and most couldn't support refugees. You might get some semi-contained towns that hadn't been connected to the wider economy but these were also just as likely to be devastated when a bank or local industry failed.
The area around Houston, Texas had the depressions effect muted by an oil boom but that employed mainly semi-skilled labour and rich oil men does not translate to employed unskilled labourers.
Really there were few other alternatives but to go west.
Honestly the places that were truly hit the least were the Native American Reservations but that was simply because they were used to having almost nothing in the first place. Many Reservations were and still are in economic disrepair.
The question you're asking though is quite different. For farmers and unskilled laborers there weren't very many choices, it didn't really matter where they went.
The Great Depression was one hell of a monster. As others have stated farmers were hit the hardest with mechanization flooding the markets (to the point that the U.S. paid farmers to burn their crops) and causing the dustbowl simultaneously and the crash of the stock market was the icing on the cake. The boom of the 20's and the use of credit evaporated when the banks emptied and the people freaked. We were already reaching a point of manufacturing more than our people could buy, even before the crash.
Here's a good source for more information
The Great Depression: 1929-1941 by Robert S. McElvaine
There's reason it took the industry of fighting a world war to break us out of that slump.