PILOT (the Pathfinder for an International Large Optical Telescope) is a proposed 2.5-m optical/infrared telescope to be located at Dome C on the Antarctic plateau. The atmospheric conditions at Dome C deliver a high sensitivity, high photometric precision, wide-field, high spatial resolution, and high-cadence imaging capability to the PILOT telescope. These capabilities enable a unique scientific potential for PILOT, which is addressed in this series of papers. The current paper presents a series of projects dealing with the nearby Universe that have been identified as key science drivers for the PILOT facility. Several projects are proposed that examine stellar populations in nearby galaxies and stellar clusters in order to gain insight into the formation and evolution processes of galaxies and stars. A series of projects will investigate the molecular phase of the Galaxy and explore the ecology of star formation, and investigate the formation processes of stellar and planetary systems. Three projects in the field of exoplanet science are proposed: a search for free-floating low-mass planets and dwarfs, a program of follow-up observations of gravitational microlensing events, and a study of infrared light-curves for previously discovered exoplanets. Three projects are also proposed in the field of planetary and space science: optical and near-infrared studies aimed at characterising planetary atmospheres, a study of coronal mass ejections from the Sun, and a monitoring program searching for small-scale Low Earth Orbit satellite debris items.