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Spiking neural networks are viable alternatives to classical neural networks for edge processing in low-power embedded and IoT devices. To reap their benefits, neuromorphic network accelerators that tend to support deep networks still have to expend great effort in fetching synaptic states from a large remote memory. Since local computation in these networks is event-driven, memory becomes the major part of the system's energy consumption. In this paper, we explore various opportunities of data reuse that can help mitigate the redundant traffic for retrieval of neuron meta-data and post-synaptic weights. We describe CyNAPSE, a baseline neural processing unit and its accompanying software simulation as a general template for exploration on various levels. We then investigate the memory access patterns of three spiking neural network benchmarks that have significantly different topology and activity. With a detailed study of locality in memory traffic, we establish the factors that hinder conventional cache management philosophies from working efficiently for these applications. To that end, we propose and evaluate a domain-specific management policy that takes advantage of the forward visibility of events in a queue-based event-driven simulation framework. Subsequently, we propose network-adaptive enhancements to make it robust to network variations. As a result, we achieve 13-44% reduction in system power consumption and 8-23% improvement over conventional replacement policies.