We study neutrino, muon, and gamma-ray fluxes in extraterrestrial environments in our Solar System via semi-analytical estimates and Monte Carlo simulations. In sites with negligible atmosphere, we find a strong reduction in the cosmic-ray-induced neutrino and muon fluxes relative to their intensities on Earth. Neutrinos with energies between 50~MeV and 100~TeV show particularly strong suppression, by as much as 10${}^3$, even at shallow depths. The solar neutrino suppression increases as the square of the site’s distance from the Sun. Natural radiation due to nuclear decay is also expected to be lower in many of these locations and may be reduced to effectively negligible levels in liquid water environments. The sites satisfying these characteristics represent an opportunity for greatly extending the physics reach of underground searches in fundamental physics, such as searches for WIMP Dark Matter, neutrinoless double-beta decay, the diffuse supernova neutrinos, and neutrinos from nearby supernova. As a potential near-term target, we propose a measurement of muon and gamma-ray fluxes in an accessible underground lunar site such as the Mare Tranquillitatis Pit to perform a first measurement of the prompt component in cosmic-ray-induced particle production, and to constrain lunar evolution models. Although the focus of this work is on fundamental physics, the finding of this work – that the existence of an atmosphere in a planet enhances cosmic-ray-induced radiation in its underground – could be relevant for a broader range of sciences, such as radiobiology deep underground and searches for extraterrestrial life.