A detailed microstructural and micromechanical study of a fly ash-based geopolymer paste including: (i) synchrotron x-ray tomography (XRT) to characterize the pores (size > 0.74 µm) that are influential in fluid transport, (ii) mercury intrusion porosimetry (MIP) to capture the volume fraction of smaller pores, (iii) high resolution scanning electron microscopy (SEM) combined with a multi-label thresholding method to identify and characterize the solid phases in the microstructure, and (iv) nanoindentation to determine the component phase elastic properties using statistical deconvolution techniques, is reported in this paper. The 3D pore structure from XRT is used in a computational fluid transport model to predict the permeability of the material. The pore volume from XRT, solid phase volumes from SEM, and the phase elastic properties are used in a numerical homogenization framework to determine the homogenized macroscale elastic modulus of the composite. The homogenized elastic moduli are in good agreement with the flexural elastic modulus determined on macroscale paste beams. It is shown that the combined use of microstructural and micromechanical characterization tools at multiple scales provides valuable information towards the material design of fly ash-based geopolymers.