This thread is interesting.
My brother holds dual US/Nigerian citizenships. He routinely travels to Nigeria several times a year. When he departs the US, he uses his US passport (which has no visa for Nigeria), and when he arrives in Lagos, presents his Nigerian passport. He has done this for 5 years and has never run into any issues. On one occasion, airline check-in asked for the visa to Nigeria, and he simply showed his Nigerian passport.
I have recently become a US citizen as well, and will use same method whenever i visit home.
I should add that my sister also holds dual UK/Nigerian passport and does the same thing whenever the travels from the UK, without any issues. And she has done this for over 15 years.
Going by some of the answers here, a dual US/Nigerian citizen would never be able to depart the US without a visa .... i doubt that is correct.
H.