Step 1: The BRICS Film Festival was launched as part of cultural exchange among BRICS nations (Brazil, Russia, India, China, South Africa).
Step 2: The first edition of the festival was held in New Delhi in September 2016.
Step 3: It showcased films from all BRICS countries, strengthening cultural diplomacy. \[ \boxed{\text{New Delhi}} \]
Considering which Indian city typically hosts major inaugural multinational cultural events helps narrow this down.
The capital city's role in hosting this inaugural international event points to option 1.
Hence, the correct answer is New Delhi.