Correlations of different azimuthal flow harmonics $v_n$ and symmetry planes $Psi_n$ can add constraints to theoretical models, and probe aspects of the system that are independent of the traditional single-harmonic measurements. Using NeXSPheRIO, a hydrodynamical model which has accurately reproduced a large set of single-harmonic correlations at RHIC, we make predictions of these new observables for 200 A GeV Au+Au Collisions, providing an important baseline for comparison to correlations of flow harmonics, which contain non-trivial information about the initial state. We also point out how to properly compare theoretical calculations to measurements using wide centrality bins and non-trivial event weighting.