Adaptive cable-driven parallel robots are a special subclass of cable-driven systems in which the locations of the pulley blocks are modified as a function of the end-effector pose to obtain optimal values of given performance indices within a target workspace. Due to their augmented kinematic redundancy, such systems enable larger workspace volume and higher performance compared to traditional designs featuring the same number of cables. Previous studies have introduced a systematic method to optimize design and trajectory planning of the moving pulley-blocks for a given performance index. In this paper, we study the motions of the pulley blocks that optimize two performance indices simultaneously: stiffness and dexterity. Specifically, we present a method to determine the pulley blocks motions that guarantee ideal dexterity with the best feasible elastic stiffness, as well as those that guarantee isotropic elastic stiffness with the best feasible dexterity. We demonstrate the proposed approach on some practical cases of planar adaptive cable-driven parallel robots.