The spin state of single magnetic atoms and molecules at surfaces is of fundamental interest and may play an important role in future atomic-scale technologies. We demonstrate the ability to tune the coupling between the spin of individual cobalt adatoms with their surroundings by controlled attachment of molecular ligands. The strength of the coupling is determined via the Kondo resonance by low-temperature scanning tunneling spectroscopy. Spatial Kondo resonance mapping is introduced as a novel imaging tool to localize spin centers in magnetic molecules with atomic precision.