  We investigate the geometric distribution of gas metallicities in the
circumgalactic medium (CGM) around $47$, $z<0.7$ galaxies from the "Multiphase
Galaxy Halos" Survey. Using a combination of quasar spectra from HST/COS and
from Keck/HIRES or VLT/UVES we measure column densities of, or determine limits
on, CGM absorption lines. We then use a Monte-Carlo Markov chain approach with
Cloudy to estimate the metallicity of cool (T$\sim$$10^4$K) CGM gas. We also
use HST images to determine host galaxy inclination and quasar--galaxy
azimuthal angles. Our sample spans a HI column density range of $13.8$ cm
s$^{-1}<{\log N_{HI}}<19.9$ cm s$^{-1}$. We find (1) while the metallicity
distribution appears bimodal, a Hartigan dip test cannot rule out a unimodal
distribution ($0.4\sigma$). (2) CGM metallicities are independent of halo mass,
spanning three orders of magnitude at fixed halo mass. (3) The CGM metallicity
does not depend on the galaxy azimuthal and inclination angles regardless of HI
column density, impact parameter and galaxy color. (4) Ionization parameter
does not depend on azimuthal angle. We suggest that the partial Lyman limit
metallicity bimodality is not driven by a spatial azimuthal bimodality. Our
results are consistent with simulations where the CGM is complex and
outflowing, accreting, and recycled gas are well-homogenized at $z<0.7$. The
presence of low metallicity gas at all orientations suggests that cold streams
of accreting filaments are not necessarily aligned with the galaxy plane at low
redshifts or intergalactic transfer may dominate. Finally, our results support
simulations showing that strong metal absorption can mask the presence of low
metallicity gas in integrated line-of-sight CGM metallicities.
