I have a business and a home in the region; Budapest to be specific. In an average week we will see no more than 2 black tourists and I am not sure that we have ever encountered a black resident. So, yes, you will be unique. But as stated above the Hungarian people are among the kindest and most generous that you will ever meet. I wouldn't hesitate for a second to recommend anyone to visit Hungary or anyplace in the region. The xenophobia comment is just name calling to avoid a frank discussion; which doesn't belong on a travel forum anyway. I doubt you will experience anything like it, but as you know it only takes one bad person and like all places on earth; the region has them. AND, unfortunately there is a growing extreme right in most of East and Western Europe that we all have to contend with.
The migrant issues are pretty much contained at the borders. While I said I rarely see a black person, I do see quite a few middle easterners and Indians and hundreds of east Asians and I am not aware of any mistreatment. Of course I don't walk in their shoes either. I am pretty sure, by and large, you will just be seen as an American tourist.
As for the Eastern vs Central labels; don't you just hate labels? In 1946 Winston Churchill gave a graduation speech at Westminster College, in Fulton, Missouri. In that speech he rightfully identified the then common classification of the region:
... Behind that line lie all the capitals of the ancient states of
Central and Eastern Europe. Warsaw, Berlin, Prague, Vienna, Budapest,
Belgrade, Bucharest and Sofia; all these famous cities and the
populations around them lie in what I must call the Soviet sphere ...
So obviously before 1946 there existed a Central Europe and Hungary had always claimed membership to that position. Then the Cold War began and the "Western" powers needed to define an enemy and Central Europe disappeared as Austria was re-categorized as West (good people) and everyone else was categorized as East (bad people). Cowboys and Indians. So these peoples wanting to regain their identity isn't laughable. Today, in the EU and the UN, depending on what program you are looking at the states can be catalogued as Eastern, Western, Central, and even South Eastern. Again, don't you just hate labels? But, I have also never met a person who became irritated because the American tourist said the wrong thing. Look at Rick Steves for instance; he promotes is Eastern European Tours. But you will impress them if you call it Central Europe. Go have fun and don't fret the details.
Now, leaving my tirade behind, this is the most amazing part of the world. Tourism is on the uptick, but enough of the region is still unaffected enough that you can still see the lands, peoples and cities in a state somewhat unpolluted by tourism. I guess Prague is the one glaring exception of this but it is still a beautiful and magnificent city. If you are into experiencing new cultures, I mean real ones, not ones fabricated for tourists, then this is the place to be and now is the time before it gets McDonalized like the rest of Europe; because it will happen.
If you include Hungary in your travels I would be pleased to help.