We assess the dominant low-redshift anisotropic signatures in the distance-redshift relation and redshift drift signals. We adopt general-relativistic irrotational dust models allowing for gravitational radiation — the `quiet universe models' — which are extensions of the silent universe models. Using cosmological simulations evolved with numerical relativity, we confirm that the quiet universe model is a good description on scales larger than those of collapsing structures. With this result, we reduce the number of degrees of freedom in the fully general luminosity distance and redshift drift cosmographies by a factor of ∼ 2 and ∼ 2.5, respectively, for the most simplified case. We predict a dominant dipolar signature in the distance-redshift relation for low-redshift data, with direction along the gradient of the large-scale density field. Further, we predict a dominant quadrupole in the anisotropy of the redshift drift signal, which is sourced by the electric Weyl curvature tensor. The signals we predict in this work should be tested with present and near-future cosmological surveys.