The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 10(8) at 1 MHz to yield the highest mechanical Qf products (>10(14) Hz) yet reported at room temperature. The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions.