We investigate surface phonon propagation in a triangular-lattice phononic crystal of microscopic holes in a gold-coated polymer by time-resolved two-dimensional imaging and by finite-element simulations at sub-gigahertz frequencies. The simulations allow the effects of exciting different points in the crystal lattice to be studied in real space, and also in k-space by spatiotemporal Fourier analysis. The acoustic field in a sub-surface plane below the reach of the holes is also revealed in real-and k-spaces. In addition, we demonstrate pitfalls in the analysis of k-space data when searching for the presence of band gaps. Applications include surface-acoustic wave filter quality control.