Understanding residential mobility and location choice is crucial for urban development and policy-making, households may partly base their decision to move from or stay at a current location on the price and quality of the available alternatives. Exploiting data from the Survey on Household Income and Wealth (SHIW) by the Bank of Italy, this study aims to understand how and the degree to which these decisions relate to each other with a focus on practical application in the Italian scenario. Alongside discrete choice models like logit model, widely employed in relevant literature, we implement decision tree techniques, specifically focusing on the random forest algorithm. These models enable a deeper understanding of the factors influencing residential mobility decisions and provide valuable insights into individual preferences and decision-making processes. This research is intended to provide significant findings for urban planning and housing policy decisions, emphasizing the direct application of findings in real-world scenarios.