We identify and phase a sample of 81 Cepheids in the maser-host galaxy NGC 4258 using the Large Binocular Telescope (LBT), and obtain calibrated mean magnitudes in up to 4 filters for a subset of 43 Cepheids using archival HST data. We employ 3 models to study the systematic effects of extinction, the assumed extinction law, and metallicity on the Cepheid distance to NGC 4258. We find a correction to the Cepheid colors consistent with a grayer extinction law in NGC 4258 compared to the Milky Way ($R_V =4.9$), although we believe this is indicative of other systematic effects. If we combine our Cepheid sample with previously known Cepheids, we find a significant metallicity adjustment to the distance modulus of $gamma_1 = -0.61 pm 0.21$ mag/dex, for the Zaritsky et al. (1994) metallicity scale, as well as a weak trend of Cepheid colors with metallicity. Conclusions about the absolute effect of metallicity on Cepheid mean magnitudes appear to be limited by the available data on the metallicity gradient in NGC 4258, but our Cepheid data require at least some metallicity adjustment to make the Cepheid distance consistent with independent distances to the LMC and NGC 4258. From our ensemble of models and the geometric maser distance of NGC 4258 ($mu_{N4258} = 29.40 pm 0.06$ mag), we estimate $mu_{LMC} = 18.57 pm 0.14$ mag ($51.82 pm 3.23$ kpc).
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