Czech For Beginners

How serious is racism in the Czech Republic?
I am a Korean-American thinking of studying abroad for a semester in Brno or Prague. I’d like to know GENERALLY how bad racism is toward Asians in those areas. I know racism is everywhere, but I’d like to know how the majority of Czechs treat Asians. Especially considering that I am American as well (beginner level at Czech), would I have problems trying to live a normal life, such as shopping, eating out, even socializing with Czech students? I don’t want to waste my time studying somewhere where everyone is rude and ignores me because of my ethnic looks.
And BTW, please don’t say something simple like, “Prague is very multicultural.” I know that, and I also know that multiculturalism doesn’t necessarily mean less racism.
I saw a few Asian tourists in Prague, I don’t believe I noticed any racism towards them.
I know there is a lot of racism towards Gypsies, that’s a fact. My partner is Mexican, and we noticed a few people giving him nasty looks. I think they thought he was Gypsy. We were stopped by a policeman who wanted to see his passport, after looking at it he sent us on our way.
I’m black, and didn’t encounter any racism while there.