We use FIRE-2 simulations to examine 3-D variations of gas-phase elemental abundances of [O/H], [Fe/H], and [N/H] in 11 Milky Way (MW) and M31-mass galaxies across their formation histories at $z leq 1.5$ ($t_{rm lookback} leq 9.4$ Gyr), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within $1$ kpc of the disk midplane is vertically homogeneous to $lesssim 0.008$ dex at all $z leq 1.5$. We find negative radial gradients (metallicity decreases with galactocentric radius) at all times, which steepen over time from $approx -0.01$ dex kpc$^{-1}$ at $z = 1$ ($t_{rm lookback} = 7.8$ Gyr) to $approx -0.03$ dex kpc$^{-1}$ at $z = 0$, and which broadly agree with observations of the MW, M31, and nearby MW/M31-mass galaxies. Azimuthal variations at fixed radius are typically $0.14$ dex at $z = 1$, reducing to $0.05$ dex at $z = 0$. Thus, over time radial gradients become steeper while azimuthal variations become weaker (more homogeneous). As a result, azimuthal variations were larger than radial variations at $z gtrsim 0.8$ ($t_{rm lookback} gtrsim 6.9$ Gyr). Furthermore, elemental abundances are measurably homogeneous (to $lesssim 0.05$ dex) across a radial range of $Delta R approx 3.5$ kpc at $z gtrsim 1$ and $Delta R approx 1.7$ kpc at $z = 0$. We also measure full distributions of elemental abundances, finding typically negatively skewed normal distributions at $z gtrsim 1$ that evolve to typically Gaussian distributions by $z = 0$. Our results on gas abundances inform the initial conditions for stars, including the spatial and temporal scales for applying chemical tagging to understand stellar birth in the MW.
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