I second what Gopunk said.
I am a Japanese-American (for classification sake) but an American through and through. I grew up in NYC probably one of the most ethnically diverse places in the US. Of course being a minority, you tend to have to face a little racism. But even now as a 32 year old I still get racial insults from blacks. It is almost never from any other group. I don't know if blacks just speak louder or their minds more freely but it always seems to be from blacks.
Mind you, I don't really have anything against blacks, I went to public school in NYC so half the kids I went to school were black. But even back then, I'd say the majority of racial insults were from blacks.
I remember an incident just several months ago walking to the subway in Times Square while going home from work. I was in my suit and carrying my briefcase and 2 black guys came up to me and said ching chong this and ching chong that and how I thought I was hot sh!t because I was wearing a suit. I was like "WTF"? Then I remember an incident a couple months before that in Grand Central Station. It was crowded and I was walking to my train. I accidentally bumped some teenage black girl and said sorry. I walked about 10 steps when all of a sudden someone kicked my feet and my shoe went flying off. I turn around and the black girl and her boyfriend are laughing at me and calling me beloved patriot this and that. Seriously, if I had been a violent person, I would have killed them since I was so much bigger than both of them but I just shook them off as ignorant youths.
This sort of stuff happens alot more than you think. I think there is a racial stereotype of asians as being non-confrontational and subserviant and to a degree, I think it is correct. I think a lot of blacks who have problems with asians know this trait and take advantage of it. From my point of view, this is where I think the asian opinion towards blacks comes from. It only takes a few negative actions for people to view entire groups in a bad light.
For me, I've been insulted by practically all racial groups, even Japanese-Japanese so maybe I'm a little immune to these actions but some people aren't as level headed as me and that is where I think these problems begin.
Just my opinion.