Two-dimensional (2D) hexagonal lattices of Cu disks are shown to induce orientation-dependent magnonic crystal (MC) modes for propagating forward volume spin waves in a single-crystal yttrium iron garnet (YIG) film. The width and depth of the magnonic band gaps are 0.022 GHz and –15.2 dB at the frequency of 1.815 GHz. Integrating differently oriented lattices on the same YIG film and positioning them between the microwave antenna surrounded by magnon absorbers consisting of Au films, we clearly resolve a characteristic frequency shift of the magnonic band gap by altering the incident angle of the spin waves to the 2D MC. The shift amounts to approximately 10 MHz when the incident angle is changed between 10° and 30°. The obtained results show a good agreement with calculations using the finite integration technique and are a step toward complete band-gap investigations in YIG of ultralow spin-wave damping.