Urban crimes are a severe threat to livable and sustainable urban environments. Many studies have investigated the patterns, causes, and strategies for curbing the occurrence of urban crimes. It is found that neighborhood socioeconomic status, physical environment, and ethnic composition all might play a role in the occurrence of urban crimes. Inspired by the recent interest in exploring urban crime patterns with spatial data analysis techniques and the development of Bayesian hierarchical analytical approaches, we attempt to explore the inherently intricate relationships between urban assaultive violent crimes and the neighborhood socioeconomic status, physical environment, and ethnic composition in Paterson, NJ, using census data of the American Community Survey, alcohol and tobacco sales outlet data, and abandoned property listing data from 2013. Analyses are set at the census block group level. Urban crime data are obtained from the Paterson Police Department. Instead of examining relationships at a global level with both non-spatial and spatial analyses, we examine in depth the potential locally varying relationships at the local level through a Bayesian hierarchical spatially varying coefficient model. At both the global and local analysis levels, it is found that median household income is decisively negatively related to urban crime occurrence. Percentage of African Americans and Hispanics, number of tobacco sales outlets, and number of abandoned properties are all positively related with urban crimes. At the local level of analysis, however, the different factors have varying influence on crime occurrence throughout the city of Paterson, with median household income having the broadest influence across the city. The practice of applying a Bayesian hierarchical spatial analysis framework to understand urban crime occurrence and urban neighborhood characteristics enables urban planners, stakeholders, and public safety officials to engage in more active and targeted crime-reduction strategies.