Both temporal and directional responses of a cavity inside a two-dimensional sonic crystal are investigated. The size of the cavity is large compared to the lattice parameter and the wavelength for the frequency range of interest. Hence, a hybrid method to compute the response is proposed, combining multiscattering theory for the calculation of the reflective properties of the sonic crystal with a modified ray-tracing algorithm for the sound propagation within the cavity. The response of this enclosure displays resonances for certain frequency bands that depend on the geometry of the lattice and the cavity. When a full band gap exists in the sonic crystal, rays cannot propagate through the medium and total reflection occurs for all incidence angles, leading to strong resonances with an isotropic intensity field inside the cavity. When only some propagation directions are forbidden, total reflection occurs for certain ranges of incidence angles, and resonances can also be elicited but with a highly anisotropic intensity field. The spectrum of resonances of the cavity is strongly affected by changes in the lattice geometry, suggesting that they can be tailored to some extent, a feature that can lead to potential applications in architectural acoustics.