We investigate the possibility that observations of ultra-high-energy cosmic rays (UHECRs) in the near future may be able to unveil their local source distribution, which will reflect observed local structures if their origins are astrophysical objects. In order to discuss this possibility, we calculate the arrival distribution of UHE protons taking into account their propagation process in intergalactic space, i.e., energy losses and deflections by the extragalactic magnetic field (EGMF). For a realistic simulation, we construct and adopt a model of a structured EGMF and UHECR source distribution, which reproduces the local structures actually observed around the Milky Way. The arrival distribution is compared statistically to the source distribution using a correlation coefficient. We find that UHECRs above 10^19.8 eV are the best indicators for deciphering the source distribution within 100 Mpc, and the detection of about 500 events on all the sky would allow us to unveil the local structure of the UHE universe for plausible EGMF strength and source number density. This number of events could be detected by 5 years observation by the Pierre Auger Observatory.