We investigate the host galaxies of compact objects merging in the local Universe, by combining the results of binary population-synthesis simulations with the Illustris cosmological box. Double neutron stars (DNSs) merging in the local Universe tend to form in massive galaxies (with stellar mass $>10^{9}$ M$_odot$) and to merge in the same galaxy where they formed, with a short delay time between the formation of the progenitor stars and the DNS merger. In contrast, double black holes (DBHs) and black hole $-$ neutron star binaries (BHNSs) form preferentially in small galaxies (with stellar mass $<10^{10}$ M$_odot$) and merge either in small or in larger galaxies, with a long delay time. This result is an effect of metallicity: merging DBHs and BHNSs form preferentially from metal-poor progenitors ($Zleq{}0.1$ Z$_odot$), which are more common in high-redshift galaxies and in local dwarf galaxies, whereas merging DNSs are only mildly sensitive to progenitors metallicity and thus are more abundant in massive galaxies nowadays. The mass range of DNS hosts we predict in this work is consistent with the mass range of short gamma-ray burst hosts.
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