Thru computer center(s) in what city or cities in the US does IB process E-mini orders on their way to exchange?

Gedman 

Thru computer center(s) in what city or cities in the US does IB process E-mini orders on their way to exchange?

Chicago or Greenwich CT, depending on where your account is hosted.
The market data gateways and the orders gateways are in Chicago for CME products but if your account is in Greenwhich (risk management) there will be some network communications and delays there (pre trade risk check).

Thank you Sam, appreciate your response very much.