Whereas clusters made of polycyclic aromatic hydrocarbon and water monomers are relevant objects in both atmospheric and astrophysical science, little is known about their energetic and structural properties. In this work, we perform global explorations of the potential energy landscapes of neutral clusters made of two pyrene units and one to ten water molecules using a Density-Functional based Tight-Binding (DFTB) potential followed by local optimisations at the Density-Functional Theory level. We discuss the binding energies with respect to various dissociation channels. It shows that cohesion energies of the water clusters interacting with a pyrene dimer is larger than that of the pure water clusters, reaching for the largest clusters an asymptotic limit similar to that of pure water clusters and that, while the hexamer and octamer can be considered as magic numbers for isolated water clusters, it is not the case anymore when they are interacting with a pyrene dimer. Ionisation potentials are also computed making use of the Configuration Interaction extension of DFTB and we show that in cations the charge is mostly carried by the pyrene molecules.