In the present work, the influence of the addition of graphene nanoplatelets presenting different dimensions on polyurethane–polyisocyanurate aerogel structure and properties has been studied. The obtained aerogels synthesized through a sol–gel method have been fully characterized in terms of density, porosity, specific surface area, mechanical stiffness, thermal conductivity, and speed of sound. Opacified aerogels showing high porosity (>92%) and low densities (78–98 kg/m3) have been produced, and the effect of the size and content of graphene nanoplatelets has been studied. It has been observed that formulations with less than 5 wt.% of graphene nanoplatelets larger than 2 microns can effectively reduce the total thermal conductivity by absorption and scattering of the infrared radiation, reducing the heat transfer by this mechanism. The resulting opacified samples are highly insulating materials, with thermal conductivities less than 18 mW/m·K. Moreover, it has been observed that smaller particles with ca. 200 nm of average length can promote an increase in the elastic modulus, therefore obtaining stiffer aerogels, combined with thermal conductivities lower than 20 mW/m·K. Results have been studied in detail, providing a further understanding of the mechanisms for improving the final properties of these materials, making them more suitable for industrial applications.