The Lunar Geophysical Network (LGN) mission is proposed to land on the Moon in 2030 and deploy packages at four locations to enable geophysical measurements for 6–10 yr. Returning to the lunar surface with a long-lived geophysical network is a key next step to advance lunar and planetary science. LGN will greatly expand our primarily Apollo-based knowledge of the deep lunar interior by identifying and characterizing mantle melt layers, as well as core size and state. To meet the mission objectives, the instrument suite provides complementary seismic, geodetic, heat flow, and electromagnetic observations. We discuss the network landing site requirements and provide example sites that meet these requirements. Landing site selection will continue to be optimized throughout the formulation of this mission. Possible sites include the P-5 region within the Procellarum KREEP Terrane (PKT; (lat: 15°; long: −35°), Schickard Basin (lat: −443; long: −551), Crisium Basin (lat: 185; long: 618), and the farside Korolev Basin (lat: −24; long: −1593). Network optimization considers the best locations to observe seismic core phases, e.g., ScS and PKP. Ray path density and proximity to young fault scarps are also analyzed to provide increased opportunities for seismic observations. Geodetic constraints require the network to have at least three nearside stations at maximum limb distances. Heat flow and electromagnetic measurements should be obtained away from terrane boundaries and from magnetic anomalies at locations representative of global trends. An in-depth case study is provided for Crisium. In addition, we discuss the consequences for scientific return of less than optimal locations or number of stations.