Hammams are more than public baths. They are places where you could forget about being a tourist and become just like anyone else. But you must go to a proper Hammam for this, not a tourist Hammam. Look for tiles around a doorway. Bring your own towel and extra underwear. Accept a massage when it is offered (all very proper) and offer it yourself. Men and women take baths separately.
How to get there
Ask around. There are plenty of hammams in the city. Look for tiled doorways.