Push Factors
Some push factors are overpopulation compared to jobs (hence a lack of jobs), military drafting, persecution by religion, air pollution, government corruption, high public debt, and a high tension between nations. Due to the increase in the world's population, the Eastern European subregion hasn't dealt with the problem of a decrease in available jobs, causing many people to leave searching for better jobs in nations such as the United States. Government corruption in nations such as Russia have caused other nations to be worried, increasing tensions between said nations. To expand more upon the persecution by religion, previously in history religions (most infamously Jews) were persecuted and driven out, and to this day persecution still remains, however it is much, much less prominent as it was in the past. Emigration from this subregion is not helping the region's already poor GDP, which has an average public debt of about 35% of each nation's GDP, as skilled workers leave due to the lower competition for jobs in locations such as Western Europe or America.
Pull Factors
All of the push factors mentioned above may push away thoughts of going to East Europe, but there are several pull factors, such as a rather mild climate and offering asylum, with one famous example being Edward Snowden. Recently with the Syrian Civil War and other crises in the Middle East, more people are immigrating into European countries, including Eastern Europe because of this asylum. They contribute to the economy by taking up jobs, and the IMF expects European countries to see a modest increase in GDP. The new immigration has also lead to Eastern Europe to have a more diverse population and thus a more diverse culture, although rather limited at this point. Though with all good things there are misconceptions and misjudgements, as there are those among the population who deem that some of these refugees are terrorists. It appears that only time with the Syrians can dispel these fears, but it seems that the granting of asylum Eastern Europe supports will hopefully affect them positively in the future.