Most African Americans who stayed did so because they had little way to leave. They had no money, no source of transportation, were almost universally illiterate, and faced the threat of violence across the region.

Additionally, the first twelve years after the Civil War, while an extremely dangerous time to be a freed person in the south, imbued former slaves with some hope that the drastic changes they were witnessing would continue. African Americans had gone from enslaved to voting citizens within two years, freedmen's schools (though severely underfunded) were being erected, and quite a number of African Americans had become local and state officeholders - some were even imbued with federal power (see LeeAnna Keith's The Colfax Massacre). Freedmen had been promised 40 acres and a mule by the government, and though this was never given en masse, some independent black societies were set up. Of course, these advancements were generally revoked after 1877, but the sense of progress they gave may have been one reason why former slaves chose to stay in the south.

Additionally, for people who essentially had no capital or raw resources, their former owners were offering one of the only feasible employment opportunities through sharecropping. This provided former slaves with housing, clothing, and a share of the crop they worked - and although sharecropping had a number of faults from the beginning and evolved into a mockery of slavery itself, it was one of the only options that freedmen had during reconstruction.

Hopefully this answer was somewhat satisfactory; again, I think it mostly comes down to a stark lack of resources.