During the past two decades, noteworthy experimental investigations have been conducted on wave propagation in phononic crystals, with special emphasis on crystals for acoustic wave control, consisting of the repetition of cylindrical or spherical elements in a fluid medium. On the other hand, the experimental characterization of the elastic wave phenomena observed in the solid microstructure of phononic crystals designed for elastic wave control has been quite sparse and limited in scope. The related literature focuses mostly on steady-state analyses that aim at highlighting filtering properties, and are limited to out-of-plane measurements. The scope of this work is to address these limitations and provide a detailed experimental characterization of the transient wave phenomena observed in the cores of lattice-like phononic crystals. This is achieved using a 3D Scanning Laser Vibrometer, which allows measuring the in-plane velocity of material points belonging to the lattice topology. This approach is tested against the benchmark case of a regular honeycomb lattice. Specifically, the objective is to demonstrate the directional and dispersive nature of the S-mode at relatively low frequencies and characterize the P-mode below and above its veering frequency. The experimental results are compared against numerical simulations and unit cell Bloch analysis to highlight similarities and differences between the true response of finite crystals and the infinite lattice approximation. This study also intends to highlight the advantages of three-dimensional laser vibrometry as a tool for the characterization of complex structural materials, while carefully exposing some limitations of this methodology.