Neuronal activity of recurrent neural networks (RNNs) experimentally observed in the hippocampus is widely believed to play a key role for mammalian ability to associate concepts and make decisions. For this reason, RNNs have rapidly gained strong interest as computational enabler of brain-inspired cognitive functions in hardware. From the technology viewpoint, nonvolatile memory devices such as phase change memory (PCM) and resistive switching memory (RRAM) have become a key asset to allow for high synaptic density and biorealistic cognitive functionality. In this work, we demonstrate for the first time associative learning and decision making in a hardware Hopfield RNN with 6 spiking neurons and PCM synapses via storage, recall and competition of attractor states. We also experimentally demonstrate the solution of a constraint satisfaction problem (CSP) namely a Sudoku with size 2×2 in hardware and 9×9 in simulation. These results support spiking RNNs with PCM devices for the implementation of decision making capabilities in hardware neuromorphic systems.