Although I am not black, I am blonde/blue eyed, so I stick out almost as much as you will there
In my 3 1/2 months, I never encountered any problems that had to do with racism. Usually if people are racist, they are racist against all non-Japanese, but hey, racists suck..who wants to talk to them anyway? As other people have said, if you venture to places outside of Tokyo, you will get stared at a lot more then I'm sure you're ever used to. The thing is though, it's almost never an angry stare, more of a "curious, wow there's actually a foreigner here", kind of stare. Most of these will come from children and gray-haired folks. I made it a point to speak in Japanese to anyone who looked afraid of me, because you'll be amazed at how much a lot of people will open up to you once they realize you can speak Japanese, and are not a zettai wakaranai gaijin (foreigner who doesn't understand anything).
I have a story I love to share about this. I was on a very crowded train going from Kyoto to Osaka. So, I, like many others, had to stand up on the train. This cute little family was standing next to me, and they had a boy and girl, no older then 9 and 7 respectively. The whole ride, they would just *STARE* at me, and I thought they were adorable, so every so often I'd glance down at them and chuckle, and they'd get embarrassed and look away for a second, and then continue to stare. At one of the stops, the train stopped kinda quickly, so we got jolted forward, and the little boy stepped on my foot. This kid's face turned white as a sheet, and was very, very, visibly afraid of what was going to happen to him next. So, without saying anything, I bent down, looked right in his eyes and said "daijoubu dakara kinishinai de (it's alright, don't worry about it) ^_^". His face was priceless
He smiled really big and started tugging at his mom, and I hear from her "ii hito dane (see, he's a good person)" I looked the mother and just started laughing, because it was so cute. End Story XD
Basically what I'm saying is, don't let your skin color stop you from going
