We present an X-ray study of the low-luminosity active galactic nucleus (AGN) in NGC 4258 using data from Suzaku, XMM-Newton, and the Swift/Burst Alert Telescope survey. We find that signatures of X-ray reprocessing by cold gas are very weak in the spectrum of this Seyfert-2 galaxy; a weak, narrow fluorescent Kα emission line of cold iron is robustly detected in both the Suzaku and XMM-Newton spectra but at a level much below that of most other Seyfert-2 galaxies. We conclude that the circumnuclear environment of this AGN is very "clean" and lacks the Compton-thick obscuring torus of unified Seyfert schemes. From the narrowness of the iron line, together with evidence of line flux variability between the Suzaku and XMM-Newton observations, we constrain the line emitting region to be between 3 × 10³ r_g and 4 × 10⁴ r_g from the black hole. We show that the observed properties of the iron line can be explained if the line originates from the surface layers of a warped accretion disk. In particular, we present explicit calculations of the expected iron line from a disk warped by Lens-Thirring precession from a misaligned central black hole. Finally, the Suzaku data reveal clear evidence of large amplitude 2-10 keV variability on timescales of 50 ksec and smaller amplitude flares on timescales as short as 5-10 ksec. If associated with accretion disk processes, such rapid variability requires an origin in the innermost regions of the disk (r 10r_g or less). Analysis of the difference spectrum between a high- and low-flux states suggests that the variable component of the X-ray emission is steeper and more absorbed than the average AGN emission, suggesting that the primary X-ray source and absorbing screen have a spatial structure on comparable scales. We note the remarkable similarity between the circumnuclear environment of NGC 4258 and another well studied low-luminosity AGN, M81*.