Presolar grains in meteorites formed in a sample of Asymptotic Giant Branch (AGB) stars that ended their lives within ≈1 Gyr of the origin of the Solar System 4.6 Gyr ago. The O-isotopic compositions of presolar O-rich stardust reflect the masses and metallicities of their parent stars. We present simple Monte Carlo simulations of the parent AGB stars of presolar grains. Comparison of model predictions with the grain data allow some broad conclusions to be drawn: (1) Presolar O-rich grains formed in AGB stars of mass ~1.15–2.2 M_⊙. The upper-mass cutoff reflects dredge-up of C in more massive AGB stars, leading to C-rich dust rather than O-rich, but the lack of grains from intermediate-mass AGB stars (>4 M_⊙) is a major puzzle; (2) The grain O-isotopic data are reproduced well if the Galaxy in presolar times was assumed to have a moderate age-metallicity relationship, but with significant metallicity scatter for stars born at the same time; (3) The Sun appears to have a moderately low metallicity for its age and/or unusual ¹⁷O/¹⁶O and ¹⁸O/¹⁶O ratios for its metallicity; and (4) The Solar ¹⁷O/¹⁸O ratio, while unusual relative to present-day molecular clouds and protostars, was not atypical for the presolar disk and does not require self-pollution of the protosolar molecular cloud by supernova ejecta.