The Totally Asymmetric Simple Exclusion Process (TASEP) has become a paradigmatic model for studying and understanding nonequilibrium systems such as traffic or transport phenomena. The TASEP with open boundaries can be defined on a one-dimensional lattice of L sites. Once a direction is fixed, particles enter with rate α from the first site, hop throughout the lattice subject to hard-core exclusion and then exit with rate β from the last site. In this work, through the use of mean-field theory, we investigate the behavior of the TASEP in the presence of local inhomogeneities, or in more detail, in which all hopping rates are uniform (and unitary) apart from a (local) region far from the boundaries in which the hopping rate is smaller, modeling a bottleneck.