Cities thrive on social interactions that foster well-being, innovation, and prosperity; yet, exogenous shocks such as pandemics, hurricanes, and wildfires can severely disrupt them. Different urban venues exhibit widely divergent response patterns, raising key questions about what factors contribute to these differences and how we can anticipate and respond. Understanding these questions is crucial for safeguarding social resilience, the capacity of urban venues to maintain both visitation and diversity. In this study, we analyze large-scale human mobility data from 15 US cities covering more than 103 million residents across three distinct urban shocks. Despite a general trend of declining visitation and weakened social mixing, 36.28%-53.01% of venues exhibit reduced segregation, and 21.04%-38.55% of venues exhibit increased visitation. By constructing a mobility network interlinking types of urban venues, we reveal that eigenvector network centrality tends to indicate the provision of essential services and robustly predicts social resilience across varied urban shocks. Specifically, centrality elevates the explanatory power by more than 80% in predicting both segregation and mobility change, compared with more intuitive features. Furthermore, compared to peripheral venues, core venues featuring shorter visit distances, broader neighborhood visitation, shorter visitor dwell times, and steadier popularity throughout the day. Such patterns imply a dual social mechanism: core venues sustain social ties through frequent informal interaction, while peripheral ones facilitate deeper engagement around specialized interests and their corresponding social circles. By bridging urban mobility research with economic theories that distinguish staple from discretionary products, we propose a well-and-pool analogy that suggests how people spend their varying urban mobility budgets.