We use fluorescence from dye-labelled polymer to measure the glass transition temperatures (T_gs) across single-layer films and near surfaces and silica interfaces in bilayer films for a series of poly(n-methacrylate)s. With nanoscale confinement, the average T_g across a film supported on silica increases for poly(methyl methacrylate) (PMMA), decreases for poly(ethyl methacrylate) (PEMA) and poly(propyl methacrylate), and is nearly invariant for poly(iso-butyl methacrylate) (PIBMA). These trends are consistent with the relative strengths of local perturbations to T_g caused by surfaces and substrates as measured in bilayer films. The substrate effect, which increases T_g via hydrogen-bonding interactions between the polymer and hydroxyl groups on the silica surface, is stronger than the free-surface effect in PMMA. The free-surface effect, which reduces T_g via a reduction in the required cooperativity of the glass transition dynamics, is stronger than the substrate effect in PEMA. The substrate and free-surface effects have similar strengths in perturbing the local T_g in PIBMA, resulting in a net cancellation of effects when measurements are made across single-layer films.