As a step toward completing and characterizing the census of the solar neighborhood, we present astrometric, photometric, and spectroscopic observations of 32 systems observed with the Cerro Tololo Inter-American Observatory 0.9 m and 1.5 m telescopes. Astrometry from the 0.9 m indicates that among the 17 systems that had no previous published trigonometric parallaxes, 14 are within 25 pc. In the full sample, nine systems have proper motions larger than 0.5"/yr, including 2MASS J02511490-0352459, which exceeds 2.0"/yr. VRI photometry from the 0.9 m and optical spectra from the 1.5 m indicate that the targets have V=11-22 mag and spectral types M3.0V-L3.0V. For 2MASS J23062928-0502285 (TRAPPIST-1), we present updated astrometry and photometric variability based on over 12 years of observations. Of the nine binaries in the sample, two promise mass determinations in the next decade: LHS 6167AB, an M4.5V system for which we present an accurate parallax placing the binary at 9.7 pc, and 2MASS J23515048-2537367AB, an M8.5V system at 21.1 pc for which we present the first evidence of an unseen, low-mass companion. Most importantly, Na I and K I gravity indicators, H{alpha} measurements, long-term photometric variability, locations on the H-R diagram, and kinematic assessments indicate that as many as 13 of the systems are young, including candidate members of young moving groups, with ages less than ~120 Myr.