Atomistic computational methods such as molecular dynamics and the Green-Kubo method are employed to shed light on the transport behavior of thermal phonons in models of graphene-based nanophononic crystals comprising periodic arrays of holes. We calculate the phonon lifetime and thermal conductivity as a function of the crystal filling fraction and temperature. The results are interpreted in terms of competition between elastic Bragg scattering and inelastic phonon-phonon scattering. We focus on the effect of the band structure on the phonon lifetime.