The first human missions on Mars will likely involve several astrobiology‐driven science operations, at sites with high biosignature preservation potential. Here, we present a study of the radiation environment induced by Galactic Cosmic Rays and Solar Energetic Particles at Oxia Planum, landing site of the European Space Agency ExoMars 2022 mission, and at two different locations in Mawrth Vallis, using the Monte Carlo GEometry ANd Tracking 4‐based code dMEREM (detailed Martian Energetic Radiation Environment Model). The radiation environment for solar minimum in 2009 and a period close to solar maximum during the declining phase of solar cycle 23 appears similar at the different sites, with the deepest Mawrth Vallis location having a slightly enhanced γ‐ray contribution, due to a higher modulation of fast neutrons by the more water‐rich regolith. The comparison with the Dose Equivalent from an updated extrapolation of 7+ years data from the Radiation Assessment Detector (RAD) onboard the Curiosity rover highlights the importance of input modulation conditions, some drawbacks of the galactic cosmic ray model used here, and the need to include heavy ions, the three aspects affecting differently the estimations for solar maximum and minimum. The dependence of doses on surface pressure highlights a possible influence of the different dust loading at the different sites. Estimated exposure levels for a 1‐year stay and for a short stay in Arabia Terra, the latter including a October 28, 2003 event with a fluence an order of magnitude higher than the relevant September 2017 event detected by RAD, leave reasonable to large safety margins.