With Gaia Data Release 2, the astronomical community is entering a new era of multidimensional surveys of the Milky Way. This new phase-space view of our Galaxy demands new tools for comparing observations to simulations of Milky Way-mass galaxies in a cosmological context, to test the physics of both dark matter and galaxy formation. We present ananke, a framework for generating synthetic phase-space surveys from high-resolution baryonic simulations, and use it to generate a suite of synthetic surveys resembling Gaia DR2 in data structure, magnitude limits, and observational errors. We use three cosmological simulations of Milky Way-mass galaxies from the Latte suite of the Feedback In Realistic Environments project, which feature self-consistent clustering of star formation in dense molecular clouds and thin stellar/gaseous disks in live cosmological halos with satellite dwarf galaxies and stellar halos. We select three solar viewpoints from each simulation to generate nine synthetic Gaia-like surveys. We sample synthetic stars by assuming each star particle (of mass 7070 M o˙) represents a single stellar population. At each viewpoint, we compute dust extinction from the simulated gas metallicity distribution and apply a simple error model to produce a synthetic Gaia-like survey that includes both observational properties and a pointer to the generating star particle. We provide the complete simulation snapshot at z = 0 for each simulated galaxy. We describe data access points, the data model, and plans for future upgrades. These synthetic surveys provide a tool for the scientific community to test analysis methods and interpret Gaia data.