Complementary electronic properties and a tendency to form sharp graphene-graphane interfaces open tantalizing possibilities for two-dimensional nanoelectronics. First-principles density functional and tight-binding calculations show that graphane can serve as natural host for graphene quantum dots, clusters of vacancies in the hydrogen sublattice. Their size n, shape, and stability are governed by the aromaticity and interfaces, resulting in formation energies approximately 1/ radicaln eV/atom and preference to hexagonal clusters congruent with lattice hexagons (i.e., with armchair edge). Clusters exhibit large gaps approximately 15/ radicaln eV with size dependence typical for confined Dirac fermions.