ABSTRACT The merger locations of binary neutron stars (BNSs) encode their galactic kinematics and provide insights into their connection to short gamma-ray bursts (SGRBs). In this work, we use the sample of Galactic BNSs with measured proper motions to investigate their kinematics and predict their merger locations. Using a synthetic image of the Milky Way and its Galactic potential we analyse the BNS mergers as seen from an extragalactic viewpoint and compare them to the location of SGRBs on and around their host galaxies. We find that the Galactocentric transverse velocities of the BNSs are similar in magnitude and direction to those of their Local Standards of Rest, which implies that the present-day systemic velocities are not isotropically oriented and the peculiar velocities might be as low as those of BNS progenitors. Both systemic and peculiar velocities fit a lognormal distribution, with the peculiar velocities being as low as ∼22–157 km s−1. We also find that the observed BNS sample is not representative of the whole Galactic population, but rather of systems born around the Sun’s location with small peculiar velocities. When comparing the predicted BNS merger locations to SGRBs, we find that they cover the same range of projected offsets, host-normalized offsets, and fractional light. Therefore, the spread in SGRB locations can be reproduced by mergers of BNSs born in the Galactic disc with small peculiar velocities, although the median offset match is likely a coincidence due to the biased BNS sample.