Motivated by cellular materials that are observed in nature and the current capabilities of additive manufacturing methods to fabricate complex designs, which has significantly raised the interest in developing architected cellular materials (ACM) for industrially-relevant high-performance components, in this contribution we propose a multiscale (FE-FFT) approach toward building mechanically optimized ACM's. We use phase-field methods for topology optimization on two different scales, by combining the inherently mass conserving Cahn-Hilliard phase separation with linear elasticity. On the macro-scale this is solved with 3 field mixed $\mathcal C^0$- continuous finite elements (FE) which allows to model an optimized structure with porosity if a smooth interface is chosen whereas on micro-scale (printing scale) a local (periodic RVE) micro-mechanical model is solved using spectral methods (FFT) using the information of macroscopic volume fraction and strain with special triply periodic minimal surface shells as initial microstructures which in the end results in optimal redistribution of the material along and around the direction of the absolute maximum principal strain. Further aspects that are discussed include improved initial guesses in the macro-scale topology optimization problem and local refinement strategies for the mapping of macroscopic information based on a selective recursive division of cells on the micro-scale. Finally, some numerical examples are presented to demonstrate the stiffness gain of structures that are modelled with the proposed two-scale framework.