Sandwich composite structures offer benefits over monolithic composites with increased bending stiffness and strength, and reduced structural weight. However, sandwich panels are more susceptible to damage from low energy impact events, such as tool drops, which can result in internal damage barely or even undetectable during visual inspection. Left undetected such damage can significantly compromise the compressive strength. An experimental study of 16-ply carbon-epoxy facesheets adhered to an aluminum honeycomb core was studied to examine the resulting failure modes in compression and the damage tolerance to low-velocity impact by quasi-static indentation. Various facesheet stacking sequences and core geometries were studied to examine the effect of facesheet and core geometry on the damage tolerance. Undamaged strength was obtained by means of an edgewise compression (EC) test. The strength of damaged specimens was obtained by compression-after-impact (CAI) test on specimens subjected to barely-visible impact damage induced by indentation of either a 25.4 or 76.2 mm diameter spherical indentor. Residual dent depths and planar delamination area for use as damage metrics were obtained from non-destructive evaluation using C-scan. Dent depth and planar delamination area results showed that the core type had a significant influence on the resistance to damage, with the denser core being more damage resistant during quasi-static indentation. Compression after impact results showed that specimens exhibited three primary failure modes, fiber failure, delamination buckling or global instability of the indentation. Although particular facesheet / core geometries had higher propensities for a particular failure mode, no definitive trend for failure mode or compressive strength for either indentor size emerges from the data.