The use of 3D printing to produce acoustic panels with good mechanical and acoustic properties was investigated in this paper. Various fiber layups of the fiberglass face sheet and core designs were fabricated and tested for their indentation resistance and acoustic absorption performance. It was found that the bidirectional face sheet layup exhibited the best indentation energy absorption recording 4.2 J, which is 37% more than the 45-degree layout and 66% more than the quasi-isotropic layup. The specific energy absorption of the hybrid honeycomb core is the best among the three core designs recording 404 J/kg, which is 56% higher than the corrugated triangle with horizontal beam core (359 J/kg) and 20% higher than double ellipse core (335 J/kg). Computed-Tomography (CT) scan was used to study the fracture behavior of the sandwich structures. It was found that the bidirectional layup exhibited a different failure mode as compared to the 45-degree and quasi-isotropic layup. In terms of the acoustic properties, the face sheets with various layup patterns have a low acoustic absorption coefficient with minimal differences from each other at low frequencies (500 Hz–3000 Hz) and have higher absorption coefficients with greater differences from each other at frequencies between 3000 Hz–6500 Hz. The absorption curve was significantly affected by the design of the core. The orientation of the core also comes into play if the core is asymmetrical. The hybrid honeycomb sandwich structure was the optimal structure among the three designs for balanced indentation resistance and acoustic insulation.