Spiking Neural Networks (SNNs) are promising bio-inspired third-generation neural networks. Recent research has trained deep SNN models with accuracy on par with Artificial Neural Networks (ANNs). Although the event-driven and sparse nature of SNNs show potential for more energy efficient computation than ANNs, SNN neurons have internal states which evolve over time. Keeping track of SNN states can significantly increase data movement and storage requirements, potentially losing its advantages with respect to ANNs. This paper investigates the energy effects of having neuron states, and how it is influenced by the chosen mapping to realistic hardware architectures with advanced memory hierarchies. Therefore, we develop STEMS, a mapping design space exploration for SNNs. STEMS models SNN's stateful behavior and explores intra-layer and inter-layer mapping optimizations to minimize data movement, considering both spatial and temporal SNN dimensions. Using STEMS, we show up to 12x reduction in off-chip data movement and 5x reduction in energy (on top of intra-layer optimizations), on two event-based vision SNN benchmarks. Finally, neuron states may not be needed for all SNN layers. By optimizing neuron states for one of our benchmarks, we show 20x reduction in neuron states and 1.4x better performance without accuracy loss.