We study the interaction between localized vibrational modes and propagating phonons in graphene nanoribbons with different types of localized internal and edge defects. We analyze discrete eigenmodes of the nanoribbons with defects and also employ direct numerical simulations of the ballistic phonon and heat transport. We observe a partial suppression of the phonon transport due to the so-called phononic Fano resonances originating from interference between localized and propagating phonons. We observe lower transmission for the defects which support larger number of localized eigenmodes. The Fano resonance is also manifested in the reduction of the heat transport along the graphene stripe, when each of the local defects reduces the amount of the heat flow transmitted through the nanoribbon, with the effect being more pronounced at low temperatures when the thermal energy transfer is dominated by the phonon transport. We also study the similar problems for edge defects in graphene nanoribbons and demonstrate that a reduction of the thermal conductivity is proportional to the length of a rough edge of the nanoribbon with edge defects.