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Disparity in suicide rates between urban and suburban/rural areas is growing, with rural areas typically witnessing higher suicide rates in the U.S. However, previous studies often ignored the effect of socio-environmental factors on the suicide rates and its regional disparity. To address these gaps, we propose a holistic data-driven framework to model the associations of social (demographic, socioeconomic) and environmental (climate) factors on suicide rates, and study the disparities across urban and suburban areas. Leveraging the county-level suicide data from 2000--2017 along with the socio-environmental features, we trained, tested and validated a suite of advanced statistical learning algorithms to identify, assess and predict the influence of key socio-environmental factors on suicide rates. Random forest outperformed all other models in terms of goodness-of-fit and predictive accuracy, and selected as the final model to make inferences. Our results indicate that population demographics is significantly associated with both urban and suburban suicide rates. We found that suburban population is more vulnerable to suicides compared to urban communities, with suburban suicide rate being particularly sensitive to unemployment rate and median household income. Our analysis revealed that suicide mortality is correlated to climate, showing that urban suicide rate is more sensitive to higher temperatures, seasonal-heating-degree-days and precipitation, while suburban suicide rate is sensitive to only seasonal-cooling-degree-days. This work provides deeper insights on interactions between key socio-environmental factors and suicides across different urbanized areas, and can help the public health agencies develop suicide prevention strategies to reduce the growing risk of suicides.