We use medium- and high-resolution spectroscopy of close pairs of quasars to analyze the circumgalactic medium (CGM) surrounding 32 damped Lyα absorption systems (DLAs). The primary quasar sightline in each pair probes an intervening DLA in the redshift range 1.6 < z abs < 3.5, such that the secondary sightline probes absorption from Lyα and a large suite of metal-line transitions (including O i, C ii, C iv, Si ii, and Si iv) in the DLA host galaxy’s CGM at transverse distances 24 kpc ≤ R ⊥ ≤ 284 kpc. Analysis of Lyα in the CGM sightlines shows an anticorrelation between R ⊥ and H i column density (N HI) with 99.8% confidence, similar to that observed around luminous galaxies. The incidences of C ii and Si ii with N > 1013 cm−2 within 100 kpc of DLAs are larger by 2σ than those measured in the CGM of Lyman break galaxies (Cf (N CII ) > 0.89 and C f ( N Si II ) = 0.75 − 0.17 + 0.12 ). Metallicity constraints derived from ionic ratios for nine CGM systems with negligible ionization corrections and N HI > 1018.5 cm−2 show a significant degree of scatter (with metallicities/limits across the range − 2.06 ≲ log Z / Z ⊙ ≲ − 0.75 ), suggesting inhomogeneity in the metal distribution in these environments. Velocity widths of C iv λ1548 and low-ionization metal species in the DLA versus CGM sightlines are strongly (>2σ) correlated, suggesting that they trace the potential well of the host halo over R ⊥ ≲ 300 kpc scales. At the same time, velocity centroids for C iv λ1548 differ in DLA versus CGM sightlines by >100 km s−1 for ∼50% of velocity components, but few components have velocities that would exceed the escape velocity assuming dark matter host halos of ≥1012 M ⊙