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?
Delhi can feel overwhelming for the bustle: escape by train to Agra and the Taj to breathe. Tokyo for its foreigness, utterly safe though even ordering food or a drink can be mind-boggling and culturally glorious: just absorb it and let people help — arigato! São Paulo for its size: get to know a local. Rio for its speed: stay long enough to catch up. Cairo for crossing the road: learn to walk like an Egyptian. New York for being New York: look for those spontaneous moments of sincerity that reveal humanity behind the sense of isolation.