To what extent did events in Eastern European countries contribute to the end of the Cold War?
Events in Eastern European countries contributed a little bit to the end of the Cold War. (They contributed a great deal if you include the Soviet Union in Eastern Europe.)
In the Soviet Union in the mid and late 1980s, Mikhail Gorbachev instituted his ideas of perestroika and glasnost. These gave Soviet citizens more economic and political freedom. This opened the door for the end of the Soviet Union as the Communist Party lost control of the people. Other countries in Eastern Europe picked up on these ideas. Most notably, the Solidarity movement came to challenge the government of Poland. This movement and others like it further weakened the communist bloc. The weakening of the Communist bloc led to the end of the Cold War.