We study three cosmological hydrodynamical simulations of Milky Way(MW)-sized haloes including a comparison with the dark matter(DM)-only counterparts. We find one of our simulated galaxies with interesting MW-like features. Thanks to a consistently tuned star formation rate and supernovae feedback we obtain an extended disc and a flat rotation curve with a satisfying circular velocity and a reasonable DM density in the solar neighbourhood. Mimicking observational methods, we re-derive the stellar mass and obtain stellar-to-halo mass ratios reduced by more than 50 per cent. We show the interaction between the baryons and the DM which is first contracted by star formation and then cored by feedback processes. Indeed, we report an unprecedentedly observed effect in the DM density profile consisting of a central core combined with an adiabatic contraction at larger galactic radii. The cores obtained are typically ˜5 kpc large. Moreover, this also impacts the DM density at the solar radius. In our simulation resembling most to the MW, the density is raised from 0.23 GeV $cm^3$ in the DM only run to 0.36 GeV $cm^3$ (spherical shell) or 0.54 GeV $cm^3$ (circular ring) in the hydrodynamical run. Studying the subhaloes, the DM within luminous satellites is also affected by baryonic processes and exhibits cored profiles whereas dark satellites are cuspy. We find a shift in mass compared to DM-only simulations and obtain, for haloes in the lower MW mass range, a distribution of luminous satellites comparable to the MW spheroidal dwarf galaxies.