Graphene, a single layer of carbon atoms tightly bound in a hexagonal honeycomb lattice to form a two-dimensional lattice, is a very interesting material with promising electronic, optical, chemical, and mechanical applicative potential [Geim and Novoselov, Nat. Mater. 6, 183 (2007)]. The properties of graphene make it suitable for a wide range of applications; however, its applicative future still depends on large scale technologies capable to robustly and reproducibly transfer its outstanding intrinsic properties into devices or complex structures. It must be recognized that a crucial technological problem, that still inhibits the applicability of high quality graphene material properties, is related to the patterning of this material using traditional top down instruments and lithographical methods. In this work, we will detail our investigations on applying a precise 30 keV Ga+ ion irradiation to selectively shape and modify a copper precursor surface for promoting the local growth of graphene surface domains. The morphology of these domains is investigated using scanning tunneling microscopy and spectroscopy to probe simultaneously the structural and the electronic properties at the atomic scale of the graphene films.