Within the semiclassical Boltzmann transport theory in the constant relaxation-time approximation, we perform an ab initio study of the transport properties of selected systems, including crystalline solids and nanostructures. A local (Gaussian) basis set is adopted and exploited to analytically evaluate band velocities as well as to access full and range-separated hybrid functionals (such as B3LYP, PBE0, or HSE06) at a moderate computational cost. As a consequence of the analytical derivative, our approach is computationally efficient and does not suffer from problems related to band crossings. We investigate and compare the performance of a variety of hybrid functionals in evaluating Boltzmann conductivity. Demonstrative examples include silicon and aluminum bulk crystals as well as two thermoelectric materials (CoSb3, Bi2Te3). We observe that hybrid functionals other than providing more realistic bandgaps-as expected-lead to larger bandwidths and hence allow for a better estimate of transport properties, also in metallic systems. As a nanostructure prototype, we also investigate conductivity in boron-nitride (BN) substituted graphene, in which nanoribbons (nanoroads) alternate with BN ones.