Magnons, quanta of spin waves, are known to enable information processing with low power consumption at the nanoscale. So far, however, experimentally realized half-adders, wave-logic and binary output operations were based on few µm-long spin waves and restricted to one spatial direction. Here, magnons with wavelengths λ down to 50 nm in ferrimagnetic Y3Fe5O12 below two-dimensional lattices of periodic and aperiodic ferromagnetic nanopillars are explored. Due to their high rotational symmetries and engineered magnetic resonances, the lattices allow short-wave magnons to propagate in arbitrarily chosen on-chip directions when excited by conventional coplanar waveguides. Performing interferometry with magnons over macroscopic distances of 350 × λ without loss of coherency, unprecedentedly high extinction ratios of up to 26 (±8) dB [31 (±2) dB] for a binary 1/0 output operation at λ = 69 nm (λ = 154 nm) are achieved in this work. The reported findings and design criteria for 2D magnon interferometry are particularly important in view of the realization of complex neuronal networks recently proposed for interfering spin waves underneath nanomagnets.