Combining eco-sustainability and technological efficiency is one of the “hot” topics in the current construction and architectural sectors. In this work, recycled tire rubber aggregates and acoustically effective fractal cavities were combined in the design, modeling, and experimental characterization of lightweight concrete hollow bricks. After analyzing the structural and acoustic behavior of the brick models by finite element analysis as a function of the type of constituent concrete material (reference and rubberized cement mixes) and hollow inner geometry (circular- and fractal-shaped hollow designs), compressive tests and sound-absorption measurements were experimentally performed to evaluate the real performance of the developed prototypes. Compared to the traditional circular hollow pattern, fractal cavities improve the mechanical strength of the brick, its structural efficiency (strength-to-weight ratio), and the medium–high frequency noise damping. The use of ground waste tire rubber as a total concrete aggregate represents an eco-friendlier solution than the ordinary cementitious mix design, providing, at the same time, enhanced lightweight properties, mechanical ductility, and better sound attenuation. The near-compliance of rubber-concrete blocks with standard requirements and the value-added properties have demonstrated a good potential for incorporating waste rubber as aggregate for non-structural applications.