Yes, the Ukraine is the best known for the Chernobyl disaster, because that was the biggest current event to come out of the country. Wherever Chernobyl happened, that area would have been known for it for a long time. Chernobyl was one of the biggest disasters in history. So many people died and the government was not honest with its own people, causing deformities and birth defects.
A disaster is worse than a human disaster. It is a nuclear disaster that we all should remember. The aftermath of the disaster is still being suffered. The world has to learn from these incidents. The future generation should understand what these means. Peace is what we want not war.
The Chernobyl accident was the largest uncontrolled radioactive release ever recorded. Twenty eight people were ultimately killed by the resulting radiation release that spanned 10 days. Up to 200,000 individuals were involved in clean up and containment activities that did not end until the Summer of 1987. A large portion of nearby communities still remain unoccupied. The first attempt at resettlement of contaminated areas did not begin until July 2010. Unfortunately, the sheer size and scope of the event necessarily means it is how Ukraine is best known.
While the Chernobyl crisis was undoubtedly a major setback for the reputation of Eastern Europe, most people still associate it with the Soviet Union, as Ukraine was under their control at the time. The current crisis in the Ukraine - where, ironically, Russia appears to be trying to reinstititute Soviet-era levels of control - is associated much more with the country than the Chernobyl Crisis.