Xenon dual-phase time projections chambers (TPCs) have proven to be a successful technology in studying physical phenomena that require low-background conditions. With 40t of liquid xenon (LXe) in the TPC baseline design, DARWIN will have a high sensitivity for the detection of particle dark matter, neutrinoless double beta decay (0 ν β β), and axion-like particles (ALPs). Although cosmic muons are a source of background that cannot be entirely eliminated, they may be greatly diminished by placing the detector deep underground. In this study, we used Monte Carlo simulations to model the cosmogenic background expected for the DARWIN observatory at four underground laboratories: Laboratori Nazionali del Gran Sasso (LNGS), Sanford Underground Research Facility (SURF), Laboratoire Souterrain de Modane (LSM) and SNOLAB. We present here the results of simulations performed to determine the production rate of ¹³⁷ Xe, the most crucial isotope in the search for 0 ν β β of ¹³⁶ Xe. Additionally, we explore the contribution that other muon-induced spallation products, such as other unstable xenon isotopes and tritium, may have on the cosmogenic background.