Almost all private Roman houses in Herculaneum and Pompeii had toilets. They were usually in the kitchens or under the stairs (Herculaneum Casa del Gran Portale house). Such solitary confinement rooms often had no doors, which would be unthinkable these days.
Interestingly, private latrines were not connected to the sewage system. It was feared that rats would get into the apartments through the pipes. Only the richer households in the Roman Empire had toilets connected to the sewage.