The development of new geopolymer foams by using construction waste can highly contribute to reducing the environmental burdens of the building industry while providing a sustainable and lightweight material for thermal and acoustic insulation. The goal of this study was to optimize the mechanical, thermal, and physical properties of geopolymer foam binders prepared only from concrete waste (CW) precursor or with ground granulated blast furnace slag (GGBS). The direct chemical foaming method was adopted using cetyl trimethyl ammonium bromide (CTAB) as a surfactant and hydrogen peroxide (H2O2) and aluminum powder (ALP) as foaming agents. The effects of using between 1 and 3% of CTAB, 3 and 9% of H2O2, and 0.01 and 0.09% of ALP on the compressive strength, density, porosity, and thermal conductivity of CW-based geopolymer foams were considered. Scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM–EDS) analyses and digital image processing techniques were employed to characterize the microstructure and quantify the open pores of the foam material. The results confirmed the possibility of preparing a stable foam geopolymer by using up to 55% of CW as a precursor, whereas achieving densities between 1.350 and 0.600 g/cm3 with corresponding compressive strengths ranging from 12.87 to 1.56 and thermal conductivities from 0.258 to 0.093 W/mK. The SEM–EDS analyses revealed the formation of various pore size distributions within the geopolymer network, in line with the thermal conductivity results of CW-based geopolymer foams.