We present all-sky simulated Fermi maps of γ-rays from dark matter (DM) decay and annihilation in the local universe. The DM distribution is obtained from a constrained cosmological simulation of the neighboring large-scale structure provided by the CLUES project. The DM fields of density and density squared are then taken as an input for the Fermi observation simulation tool to predict the γ-ray photon counts that Fermi would detect in 5 years of an all-sky survey for given DM models. Signal-to-noise ratio (S/N) sky maps have also been obtained by adopting the current Galactic and isotropic diffuse background models released by the Fermi Collaboration. We point out the possibility for Fermi to detect a DM γ-ray signal in local extragalactic structures. In particular, we conclude here that Fermi observations of nearby clusters (e.g., Virgo and Coma) and filaments are expected to give stronger constraints on decaying DM compared to previous studies. As an example, we find a significant S/N in DM models with a decay rate fitting the positron excess as measured by PAMELA. This is the first time that DM filaments are shown to be promising targets for indirect detection of DM. On the other hand, the prospects for detectability of annihilating DM in local extragalactic structures are less optimistic even with extreme cross-sections. We make the DM density and density squared maps publicly available online.