When Pelourinho was developed for tourists, locals were made to move their real lives. Since then, contiguous streets with views and character have been heavily developed for tourist pousadas. In the area, you will see real life up close as local kids who are sent there to beg and other locals hoping to profit from tourists solicit you. You can go off the beaten path to some smaller real life side streets and make your contribution to support the real local economy by "direct transfer".
However, you need not stay "out of town". There are residential neighborhoods nearby, like Barra and Rio Vermelho, that have tourist hotels/pousadas/hostels, as well as apartments for locals and tourists.