Path planning, critical to mobile robot autonomy, is an essential component of long-range navigation that seeks to determine the sequence of steps required to reach a goal based on prior encoding of the environment. Our current neurobiological understanding of such a pathfinding process comes from the research on hippocampal place cells. We use an interconnected network of spiking neurons to model place cells as a cognitive graph. Stimulation of the place cell that represents the goal location causes activation of place cells through spike propagation on the network. We describe neural networks that could be used to decode this spiking activity to select the direction for movement. Two models of synaptic-dependent spike latency are compared and their influence on path planning is illustrated using examples implemented with a neuromorphic VLSI circuit.