Nuclear magnetic resonance (NMR) data for graphenes are mainly lacking in the literature. We provide quantitative first-principles quantum-chemical calculations of NMR chemical shifts and shielding anisotropies as well as spin-spin couplings and anisotropies for increasingly large, hexagon-like fragments of graphene, hydrogenated graphene (graphane) and fluorinated graphene (fluorographene). Due to the rapid convergence of finite molecular model results, the parameter values in the innermost region of large flakes of these materials approach the bulk limit. For nuclear shieldings in the finite band-gap graphane and fluorographene systems, as well as deuterium quadrupole couplings in graphane, these limiting values are verified by periodic gauge-including projector augmented wave (PAW) calculations at corresponding theoretical levels. The periodic PAW wave method was used for all systems to obtain periodic structures. A quantum-chemical cluster approach was used with novel completeness-optimised basis sets to calculate both the shielding and coupling tensors for planar carbon nanoflakes of increasing size. The geometry of the innermost part of the nanoflakes as well as the nuclear shieldings converge toward the periodic counterparts. The cluster method allows the calculation of the spin-spin coupling tensors of all the graphenes and--in contrast to the periodic approach--all the NMR properties for the zero-band-gap graphene itself. The obtained parameters provide a plausible starting point for experimental NMR investigations of graphenes.