Areas where people of color should avoid?
I'm planning a road trip that will take me through 25-30 states and I'm Asian. Are there towns, counties, and or states I should avoid?
Depends on the individual
....you shouldn't have any trouble anywhere in the country, though as with anything in life there are always exceptions. Keep in mind that this would be a function of an individual's mentality, and not necessarily a reflection on all people in a given community. There are all kinds, from what you're fearing to those who dislike any vehicle (and by extension, those who drive them) but those made by, ie, Dodge.
The chance of meeting someone whom would do you harm is quite slim, though watching certain movies you'd be forgiven for thinking that all small towns are made up of a stereotypical population of thugs and crooked police asking "What chew doon here, boyah?", or that all cities are rife with stunt-driving motorcycle-riding gangstas that will kill for gold fillings.
Where I live and work, for example, you could say there are a lot of racist, prejudicial people, but I don't recall there being any racial crimes in the last 10 years. And they don't reflect the silent majority of honest, hardworking people.
Now, as far as areas of certain cities/towns that should be avoided for personal safety no matter what color you are, that's another story entirely. Your best bet is to go on instinct. Seedy bars generally contain a collection of like-minded people, and the same can be said for certain areas of cities. You may be seen as an interloper in a predominately (insert other ethnic group) section of a city, arousing suspicion. My first time walking in Boston, I 'stumbled' into a bad section...all of the sudden, everything was very quiet, shady characters all around. I knew I should turn around, and that's what I did.
Places to Avoid
There are some very racist people in every city, county, and state in this country. There are also very good-hearted people in the same locales. The good news is that there are more of the latter, and for the most part they keep the former in check, particularly in public places. You might get a nasty look here and there, or a demeaning attitude or remark from an ignorant person, but the chances of running into a dangerous situation are minute at best. Try to stick to the interstate highways. You will have many options for towns and cities that are used to people of all colors and creeds passing through.
Try to spend more time planning on where you want to go and what you want to see rather than worrying about the little things. If you want information about specific routes and places, just post another thread. You'll get plenty of feedback.