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?
Any major Chinese city during the October national holidays. It takes 2-5 times longer than normal to travel even short distances. October holidays are amateur hour and brain dead drivers will behave in new and increasingly dangerous ways on the roads as tempers flare. Public transit is clogged with confused out of towners. Every restaurant of note will be packed 3 days before, 3 days after and all of the holidays. Getting in at Pizza Hut can be tricky. If not sold out completely, even minor attractions will be completely unenjoyable due to crowding and general claustrophobia.
Bars and clubs are packed which may be a good thing depending on your tastes. Hell even grocery stores are crowded.
The public bathrooms are …… woefully under maintained for the sudden surge in visitors. Like you can see a second pile where people started going after the pile that formed on top of the clogged toilet reached ass height.