Monitoring neuronal activity with simultaneously high spatial and temporal resolution in living cell cultures is crucial to advance understanding of the development and functioning of our brain, and to gain further insights in the origin of brain disorders. While it has been demonstrated that the quantum sensing capabilities of nitrogen-vacancy (NV) centers in diamond allow real time detection of action potentials from large neurons in marine invertebrates, quantum monitoring of mammalian neurons (presenting much smaller dimensions and thus producing much lower signal and requiring higher spatial resolution) has hitherto remained elusive. In this context, diamond nanostructuring can offer the opportunity to boost the diamond platform sensitivity to the required level. However, a comprehensive analysis of the impact of a nanostructured diamond surface on the neuronal viability and growth was lacking. Here, we pattern a single crystal diamond surface with large-scale nanopillar arrays and we successfully demonstrate growth of a network of living and functional primary mouse hippocampal neurons on it. Our study on geometrical parameters reveals preferential growth along the nanopillar grid axes with excellent physical contact between cell membrane and nanopillar apex. Our results suggest that neuron growth can be tailored on diamond nanopillars to realize a nanophotonic quantum sensing platform for wide-field and label-free neuronal activity recording with sub-cellular resolution.