Title pretty much states the question. How much hotter do air conditioning units make it outside in a large city like NYC, Chicago, etc?
This isn't a direct answer, but a relevant comment on the question that is too long to be a comment on this system.
The heating you seem to be considering is only about total electrical power dissipated. Whether some of that is used for air conditioning is irrelevant. In the steady state, the cooled buildings will cool the air, except for the power used to run the air conditioners. A air conditioner that consumes 1 kW of electrical power will cause the same overall heating in steady state as a 1 kW electrical space heater or toaster or hair dryer. In the short term, the air conditioner moves heat from inside to outside, but in the long term that heat gets back inside.
The real question is therefore how much electrical consumption increases the averge air temperature. You should be able to get figures for electrical consumption by doing a little digging. However, relating that power to temperature rise will be tricky. To take some stab at it you have to make some assumption about how much air is flowing around the city, which of course varies dramatically with wind. Pick some representative wind speed, pick some height, then calculate the mass of new air that has to be heated per unit of time. That will give you nice and neat figure for what is at best a wild-ass guess.
Note that dissipation of electrical power in a city is probably a small contribution to the local temperature rise. The stone and asphalt heated by the sun without the benefit of evaporative cooling like leaves have is very likely a much larger factor.
The temperature rise in cities has been measured, so you could do the heated air flow analisys in reverse and take a stab at the extra power required to heat the air. I think you'll find that is way more than the total electrical power delivered to the city. All those car and truck engines sitting in traffic probably add up to more heating power than the delivered electrical power, but I'm still guessing that the solar power not countered by evaporative cooling of leaves dominates by a lot.
Have a look at urban heat effect.
An interesting study is the effect of urban heat islands on temperature measurements and the trend of global warming due to bad siting of the temperature sensors.