I've met a few black guys/girls in Japan and none of them was complaining about racism issues. That said, I am not saying that racism does not exist in Japan. You might get very unlucky and end up in a racist environment, but this is not the norm and it could happen in just any other country.
Japan does not have the same history as you guys have in America, and all foreigners are more or less considered the same here (this is a very approximate statement but it would require pages to fully explain).
I don't think you will have any problem in everyday life, as long as you make the effort to learn the customs and adapt to the Japanese lifestyle.
If you're interested in asking the question to another black guy who lived in Japan, I suggest you contact my friend Jonathan through his blog at
Jonathan's Japan Journal • ジョナサンの日本日記.
PS: When it comes to women, yes, foreign men are quite popular here and black men are no exception