First of all, please forgive my bad english.
I am actually from Hong Kong, and that's the reason why I don't know
much about the US policy on chaning auto's color.

I am right now living in Chicago, IL. However my car was registered at
Nashville, TN. Anyway, I really hate the color of my car, I want her
to have some new paint. What is the procedure for that? Do I need to
file this to the DMV? Which one should I goes to, the IL one or the TN
one?

You need to go to the DMV in Chigaco to re-register your car if you
plan to live there. Usually, when moving to a new state you hav 90
days to register your car there. When filling out the forms, you
should make the appropriate change in color on the forms.

Please note that when you get your car repainted, you should spend
some more money and get it done right. The shop should sand, primer,
and then paint your car. It is also VERY important that you have a
clearcoat applied on top of the paint layer, as it will prevent
premature damage caused by abrasions and sunlight