You can investigate some of the causes of the fall of the Soviet Union for a project. Consider the nationalist movements that first occurred in the Baltic region, when countries like Latvia demanded autonomy, and ways in which this dissent weakened the central government. Another idea is to analyze the failed coup of 1991: Why did this cause an uproar, and why were its organizers unable to quell the popular protests? You could also compare and contrast these events and consider which was more influential in the fall of the Soviet Union.
Another idea for a project is to investigate the Soviet Union's economy and ways in which it contributed to the Soviet Union's collapse. Once elected, Soviet leader Mikhail Gorbachev initiated a series of economic reforms as part of the perestroika, or reconstruction. You could research a specific part of these reforms, such as the leasing of land to farmers, or the decline in military spending or reasons these reforms, taken together, ultimately caused the Soviet Union's economic collapse.
Demographic trends were also important in the fall of the Soviet Union and can provide the basis for a project. According to Kathryn Stoner-Weiss of Harvard University, the population decline of around 50 percent between 1960 and 1980 created a need for workers and an increasing number of pensioners. In the same period, life expectancy and the standard of living also declined, while alcoholism rates soared. You can explore one of these issues individually, compare and contrast with countries across Europe or consider how Gorbachev's reforms failed to meet the Soviet Union's social needs.
You can also consider the effects of the fall of the Soviet Union for a project. You could focus on the creation of the the new entity comprising most of the former Soviet countries, the Commonwealth of Independent States, which was formed in 1992. Although each country is independent, they are linked by economic and sometimes military ties. Another idea is to focus on the impact that the collapse of the Soviet Union had on a specific country. In Russia, for example, the end of the Soviet era witnessed the beginning of new economic reforms, characterized by soaring inflation rates, the rise of oligarchs and problems with corruption and organized crime.