We present an initial survey of Mg II absorption characteristics in the halos of a carefully constructed, volume-limited subsample of galaxies embedded in the spectroscopic part of the Sloan Digital Sky Survey (SDSS). We observed quasars near sightlines to 20 low-redshift (z ~ 0.1), luminous (M _r + 5log h ≤–20.5) galaxies in SDSS DR4 and DR6 with the LRIS-B spectrograph on the Keck I telescope. The primary systematic criteria for the targeted galaxies are a redshift z 0.1 and the presence of an appropriate bright background quasar within a projected 75 h ^–1 kpc of its center, although we preferentially sample galaxies with lower impact parameters and slightly more star formation within this range. Of the observed systems, six exhibit strong (W _eq(2796) ≥ 0.3 Å) Mg II absorption at the galaxy's redshift, six systems have upper limits which preclude strong Mg II absorption, while the remaining observations rule out very strong (W _eq(2796) ≥ 1-2 Å) absorption. The absorbers fall at higher impact parameters than many non-absorber sightlines, indicating a covering fraction f_c 0.4 for ≥0.3 Å absorbers at z ~ 0.1, even at impact parameters ≤35 h ^–1 kpc (f _c ~ 0.25). The data are consistent with a possible dependence of covering fraction and/or absorption halo size on the environment or star-forming properties of the central galaxy.