In this paper, we study the radiation from embedded sources in two-dimensional finite-size ``photonic-quasicrystal’’ (PQC) slabs made of dielectric rods arranged according to a 12-fold symmetric aperiodic tiling. The results from our investigation, based on rigorous full-wave simulations, show the possibility of achieving broadside radiation at multiple frequencies, with high directivity (e.g., 15 dB) and low sidelobes (e.g., -12 dB). We also show that leaky waves are supported by a PQC slab and that the beamwidth is directly proportional to the leaky wave attenuation constant, which provides a physically incisive interpretation of the observed radiation characteristics.