I thought parts of it were Chicago, and parts Pittsburgh?
The full list, via IMDB. I think the city scenes were mainly NYC and Pittsburgh.
Downtown, Los Angeles, California, USA
El Camino College, Torrance, California, USA
(Bike Chase and Reactor)
Cairngorms National Park, Scotland, UK
Cardington Airship Hangars, Bedfordshire, England, UK
(studio)
Carnegie Mellon University - 5000 Forbes Avenue, Pittsburgh, Pennsylvania, USA
George Farmiloe Building - 28-36 St John Street, Clerkenwell, London, England, UK
(Police HQ)
Scotland, UK
Greenwood Lake, New York, USA
Heinz Field - 100 Art Rooney Avenue, Pittsburgh, Pennsylvania, USA
Inverness Airport, Dalcross, Highland, Scotland, UK
Jodhpur, Rajasthan, India
London, England, UK
Los Angeles, California, USA
Mehrangarh Fort, Jodhpur, Rajasthan, India
Mellon Institute, Pittsburgh, Pennsylvania, USA
Metro-Goldwyn-Mayer Studios, Hollywood, Los Angeles, California, USA
(studio)
New York City, New York, USA
Newark, New Jersey, USA
Nottingham, Nottinghamshire, England, UK
Osterley Park House, Isleworth, Middlesex, England, UK
(Wayne Manor)
Pittsburgh, Pennsylvania, USA
Queensboro Bridge, Manhattan, New York City, New York, USA
Quincy, Illinois, USA
The Farmiloe Building, 34 St John Street, London, England, UK
(Gotham City Police Department)
Turda Saline, Cluj, Romania
Warner Brothers Burbank Studios - 4000 Warner Boulevard, Burbank, California, USA
(studio)
Wollaton Hall, Nottingham, Nottinghamshire, England, UK
(Wayne Manor)