We present results from an optical search for Local Group dwarf galaxy candidates associated with the Ultra-Compact High Velocity Clouds (UCHVCs) discovered by the ALFALFA neutral hydrogen survey. The ALFALFA UCHVCs are isolated, compact H i clouds with projected sizes, velocities, and estimated H i masses that suggest they may be nearby dwarf galaxies, but that have no clear counterpart in existing optical survey data. We observed 26 UCHVCs with the WIYN 3.5 m telescope and One Degree Imager (ODI) in two broadband filters and searched the images for resolved stars with properties that match those of stars in typical dwarf galaxies at distances <2.5 Mpc. We identify one promising dwarf galaxy candidate at a distance of ∼570 kpc associated with the UCHVC AGC 268071, and five other candidates that may deserve additional follow-up. We carry out a detailed analysis of ODI imaging of a UCHVC that is close in both projected distance and radial velocity to the outer-halo Milky Way globular cluster Pal 3. We also use our improved detection methods to reanalyze images of five UCHVCs that were found to have possible optical counterparts during the first phase of the project, and confirm the detection of a possible stellar counterpart to the UCHVC AGC 249525 at an estimated distance of ∼2 Mpc. We compare the optical and H i properties of the dwarf galaxy candidates to the results from recent theoretical simulations that model satellite galaxy populations in group environments, as well as to the observed properties of galaxies in and around the Local Group.