We perform molecular dynamics simulations of a bead-spring polymer melt surrounding a nanoscopic particle. We explore the effect of the polymer/nanoparticle interactions, surface-to-volume ratio, and boundary conditions on both the structure and dynamics of the polymer melt. We find that the chains near the nanoparticle surface are elongated and flattened and that this effect is independent of the interaction for the range of interactions we study. We show that the glass transition temperature T-g of the melt can be shifted to either higher or lower temperatures by tuning the interactions between polymer and nanoparticle. A gradual change of the polymer dynamics approaching the nanoparticle surface causes the change in the glass transition. The magnitude of the shift is exaggerated by increasing fraction of surface monomers in the system. These behaviors support a "many-layer"-based interpretation of the dynamics. Our findings appear applicable to systems in which surface interactions dominate, including both traditional and nanofilled polymer melts, as well as systems with markedly different geometries, such as ultrathin polymer films. In particular, we show how our results might be compared with those obtained from experimental studies of "bound" polymer.