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Dark matter (DM) direct detection experiments aim to place constraints on the DM--nucleon scattering cross-section and the DM particle mass. These constraints depend sensitively on the assumed local DM density and velocity distribution function. While astrophysical observations can inform the former (in a model-dependent way), the latter is not directly accessible with observations. Here we use the high-resolution ARTEMIS cosmological hydrodynamical simulation suite of 42 Milky Way-mass halos to explore the spatial and kinematical distributions of the DM in the solar neighbourhood, and we examine how these quantities are influenced by substructures, baryons, the presence of dark discs, as well as general halo-to-halo scatter (cosmic variance). We also explore the accuracy of the standard Maxwellian approach for modelling the velocity distribution function. We find significant halo-to-halo scatter in the density and velocity functions which, if propagated through the standard halo model for predicting the DM detection limits, implies a significant scatter about the typically quoted limit. We also show that, in general, the Maxwellian approximation works relatively well for simulations that include the important gravitational effects of baryons, but is less accurate for collisionless (DM-only) simulations. Given the significant halo-to-halo scatter in quantities relevant for DM direct detection, we advocate propagating this source of uncertainty through in order to derive conservative DM detection limits.