By this I mean the overstimulation of the senses that happens while you are there.

My answer is probably Old Delhi. From the sheer population density, the near-constant honking, the utter chaos on the streets, the panoply of religions and ethnicities, the myriad scents and colours that pass you by as you travel down the narrow lanes, and not least the choking air pollution, it is certain to keep you on edge, not necessarily in a bad way.

Are there other cities that come close to, or even surpass, this?