Calcite is among the most abundant minerals on earth and plays a central role in many environmental and geochemical processes. Here we used amplitude modulation atomic force microscopy (AFM) operated in a particular regime to visualize single ions close to the (10 (1) over bar4) surface of calcite in solution. The results were acquired at equilibrium, in aqueous solution containing different concentrations of NaCl, RbCl, and CaCl2. The AFM images provide a direct and atomic-level picture of the different cations adsorbed preferentially at certain locations of the calcite water interface. Highly ordered water layers at the calcite surface prevent the hydrated ions from directly interacting with calcite due to the energy penalty incurred by the necessary restructuring of the ions' solvation shells. Controlled removal of the adsorbed ions from the interface by the AFM tip provides indications about the stability of the adsorption site. The AFM results show the familiar "row pairing" of the carbonate oxygen atoms, with the adsorbed monovalent cations located adjacent to the most prominent oxygen atoms. The location of adsorbed cations near the surface appears better defined for monovalent ions than for Ca2+, consistent with the idea that Ca2+ ions remain further away from the surface of calcite due to their larger hydration shell. The precise distance between the different hydrated ions and the surface of calcite is quantified using MD simulation. The preferential adsorption sites found by MD as well as the ion residence times close to the surface support the AFM findings, with Na+ ions dwelling substantially longer and closer to the calcite surface than Ca2+. The results also bring new insights into the problem of the Stern and electrostatic double layer at the surface of calcite, showing that parameters such as the thickness of the Stern layer can be highly ion dependent.