We present an analysis of the $R\lesssim 1.5$ kpc core regions of seven simulated Milky Way mass galaxies, from the FIRE-2 (Feedback in Realistic Environments) cosmological zoom-in simulation suite, for a finely sampled period ($\Delta t = 2.2$ Myr) of 22 Myr at $z \approx 0$, and compare them with star formation rate (SFR) and gas surface density observations of the Milky Way's Central Molecular Zone (CMZ). Despite not being tuned to reproduce the detailed structure of the CMZ, we find that four of these galaxies are consistent with CMZ observations at some point during this 22 Myr period. The galaxies presented here are not homogeneous in their central structures, roughly dividing into two morphological classes; (a) several of the galaxies have very asymmetric gas and SFR distributions, with intense (compact) starbursts occurring over a period of roughly 10 Myr, and structures on highly eccentric orbits through the CMZ, whereas (b) others have smoother gas and SFR distributions, with only slowly varying SFRs over the period analyzed. In class (a) centers, the orbital motion of gas and star-forming complexes across small apertures ($R \lesssim 150$pc, analogously $|l, Comment: 9 pages, 3 figures, accepted to ApJ Letters. One appended supplemental appendix and figure, which do not appear in the ApJ version