This study maps the challenges public governance faces in its mission to ensure a high level of societal well-being in European countries due to complex and multidimensional analysis, both on scientific and economic levels: bibliometric analysis, vector quantisation mapping, and clustering analysis of countries. The proposed research advocates considering relevant descriptors of the two phenomena, namely the six dimensions of public governance and the composite quality of life index, to analyse their interdependence by 2020, the year for which official statistics reveal data. Our research proposes a classification of the European Union Member States from the perspective of the progress made at the governmental decision-making level for the multidimensional approach to quality of life to identify the models of good practice. The methodological support was offered by cluster analysis and a vector quantisation method, namely K-means. KNIME software has allowed us to connect to various data sources visually. Clustering of European countries has revealed several disparities thus, Denmark and Finland (which are countries with a high level of quality of life) are examples of good practices, while countries such as Romania and Bulgaria are facing difficulties in significantly improving their quality of life due to the deficiencies of the governing act. Finally, the research highlights the channels through which public governance can substantially contribute to societal well-being, keeping in mind the relatively low importance of welfare given to formal aspects of democratic representation compared to the extent of quality governance.