In this paper, a computational study of Li, Na, and K adsorption and migration on pristine and defective graphene surfaces is conducted to gain insight into the metal storage and mobility in carbon-based anodes for alkali metal batteries. Atomic level studies of the metal adsorption and migration on the graphene surface can help address the challenges faced in the development of novel alkali metal battery technologies, as these systems act as convenient proxies of the crystalline carbon surface in carbon-based materials including graphite, hard carbons and graphene. The adsorption of Li and K ions on the pristine graphene surface is shown to be more energetically favourable than Na adsorption. A collection of defects expected to be found in carbonaceous materials are investigated in terms of metal storage and mobility, with N- and O-containing defects found to be the dominant defects on these carbon surfaces. Metal adsorption and migration at the defect sites show that defect sites tend to act as metal trapping sites, and metal diffusion around the defects is hindered when compared to the pristine surface. We identify a defect where two C sites are substituted with O and one C site with N as the dominant surface defect, and find that this defect is detrimental to metal migration and hence the battery cycling performance.