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Ensuring public safety in a Smart City (SC) environment is a critical and increasingly complicated task due to the involvement of multiple agencies and the city's expansion across cyber and social layers. In this paper, we propose an extensive form perfect information game to model interactions and optimal city resource allocations when a Terrorist Organization (TO) performs attacks on multiple targets across two conceptual SC levels, a physical, and a cyber-social. The Smart City Defense Game (SCDG) considers three players that initially are entitled to a specific finite budget. Two SC agencies that have to defend their physical or social territories respectively, fight against a common enemy, the TO. Each layer consists of multiple targets and the attack outcome depends on whether the resources allocated there by the associated agency, exceed or not the TO's. Each player's utility is equal to the number of successfully defended targets. The two agencies are allowed to make budget transfers provided that it is beneficial for both. We completely characterize the Sub-game Perfect Nash Equilibrium (SPNE) of the SCDG that consists of strategies for optimal resource exchanges between SC agencies and accounts for the TO's budget allocation across the physical and social targets. Also, we present numerical and comparative results demonstrating that when the SC players act according to the SPNE, they maximize the number of successfully defended targets. The SCDG is shown to be a promising solution for modeling critical resource allocations between SC parties in the face of multi-layer simultaneous terrorist attacks.