Two local reactivity descriptors computed by Kohn-Sham density functional theory (DFT) are used to predict and rationalize interactions of nucleophilic molecules (exemplified by CO and H2O) with transition metal (TM) and oxide surfaces. The descriptors are the electrostatic potential, V-S(r), and the local electron attachment energy, E-S(r), evaluated on surfaces defined by the 0.001 e Bohr(-3) isodensity contour. These descriptors have previously shown excellent abilities to predict regioselectivity and rank molecular as well as nanoparticle reactivities and interaction affinities. In this study, we generalize the descriptors to fit into the framework of periodic DFT computations. We also demonstrate their capabilities to predict local surface propensity for interaction with Lewis bases. It is shown that E-S(r) and V-S(r) can rationalize the interaction behavior of TM oxides and of fcc TM surfaces, including low-index, stepped and kinked surfaces spanning a wide range of interaction sites with varied coordination environments. Broad future applicability in surface science is envisaged for the descriptors, including heterogeneous catalysis and electrochemistry.