There have been racial attacks on immigrants of Asian and African descent in the Ukraine in the past but one cannot generalise these sentiments across the entire population. I doubt the racism of a few people will affect your boyfriend in his day to day life.
Corruption is an issue in the Ukraine, especially amongst the police. But again, one cannot let the bad behaviour of a few deter you from making a life in the Ukraine.
Perhaps have a look at page Moving to Ukraine which will give you an overview of the country and a brief insight into what it might be like to live there.
Best of luck with your move