We present a workflow for the inverse design of architected materials with targeted effective mechanical properties. The approach leverages a low-dimensional descriptor space to represent the topology and morphology of complex mesostructures, enabling efficient navigation within the design space. Data for training is generated through numerical homogenization using a Fast Fourier Transform (FFT)-based solver, providing high-fidelity mappings from structural descriptors on the mesoscale to effective properties. A neural network (NN)-based surrogate model is trained to approximate this mapping. The inverse design task is then formulated as an optimization problem over the descriptor space, where gradient-based optimizers are applied to identify the descriptors, the inputs of the surrogate. We focus on the case of anisotropic linear elasticity and demonstrate the method using spinodoid architected materials, which offer tunable anisotropy and a low-dimensional descriptor space. The framework is validated for the inverse design targeting the anisotropic stiffness of a femoral bone sample. In addition, we propose a method to determine the anisotropy class of a given stiffness tensor. This enables a quantitative evaluation of how closely the bone's anisotropy class can be approximated by spinodoids. We analyze the influence of the optimization loss function on the inverse design outcome by comparing results across different losses. Ultimately, a logarithmic loss function is chosen, as it enables simultaneous optimization of the stiffness and compliance.