While Hyderabad’s Ramoji Film City holds the record of world’s largest integrated film city, the western world took interest in other places while filming some of their shots in India. The land of former kings and Rajput palaces, the state of Rajasthan (which literally means ‘Land of Kings’) is one of the favourite filming locations of Hollywood. But let’s brief about Indian involvement in Hollywood and the love and fascination of filmmakers for India.
Indian themes and locations have been exotically exploited in film industry back to the days of British imperialism. Hollywood had tasted Indian flavour for the first time in 1935 in the film The Lives of a Bengal Lancer, which although had an Indian theme, but was filmed entirely in Hollywood studios. The second film The Rains Came, which was again not filmed in India, but was based on the novel The Rains Came by Louis Bromfield in 1937. It involved an Indian theme and the film was entirely shot in Hollywood studies. Perhaps it was the British cinema which filmed for the first time in a remote village near Darjiling (Darjeeling) in 1947. The film directed by Micheal Powell and Emeric Pressburger was known as The Black Narcissus. Soon after India’s independence and partition (the same year in 1947), river Ganges (Ganga) witnessed filming of the French film The River (Le Fleuve) in 1951. Following this, Hollywood stepped into applying Indian themes in their movies. Films such as Bhowani Junction (1956), Carry On….Up the Khyber (1968), The Man who would be King (1975), Indiana Jones and the Temple of Doom (1984) etc. had Indian themes, but were filmed in non-Indian locations such as Pakistan, Khyber Pass (Pakistan-Afghanistan), Wales, Sri Lanka etc. Perhaps the usage of actual Indian locations became more profound in late 20th and current 21st century Hollywood films such as Gandhi (1982), Octopussy (1983), Passage to India (1984), City of Joy (1992), Outsourced (2006), The Namesake (2006), The Darjeeling Limited (2007), A Mighty Heart (2007), Slumdog Millionaire (2008), The Other End of the Line (2008), Eat Pray Love (2010), The Best Exotic Marigold Hotel (2011), Mission Impossible – Ghost Protocol (2011), Zero Dark Thirty (2012), The Dark Knight Rises (2012), Life of Pi (2012) and lastly, Singularity (2013).
To make it much simpler, here is a map designed by me pointing out the film and its locations across the country. 
Source:
https://www.quora.com/Which-all-are-the-Hollywood-movies-with-an-Indian-backdrop
http://www.scoopwhoop.com/entertainment/india-in-hollywood/
Map designed by self. Original map copyrighted by d-maps.com
Abnormally Perfect 