We report the formation of novel mesoscopic two-dimensional bubble structures coexisting with nanometer-scale, two monolayer high, meandering islands of characteristic separation approximately 11 nm on CaF2(111) surfaces exposed to glancing incidence ion beam irradiation (4 degrees, 4.5 keV Ar+). The island and bubble structures can be explained, respectively, by nanoscale stress domain related local self-ordering of a single calcium adlayer on phase-separated F- (fluorine ion) and F-center (color center) terminated mesoscopic domains.