Step 1: Understanding the Concept:
India built its nuclear power programme in stages from the 1960s onward, and the very first commercial nuclear power station is a well known fact in Indian energy geography.
Step 2: Identify the plant.
The Tarapur Atomic Power Station, in Maharashtra, was commissioned in 1969 with help from the United States and is India's first nuclear power station. It still operates today with newer units added over time.
Step 3: Why the other options are wrong:
Kalpakkam (Tamil Nadu), Narora (Uttar Pradesh) and Kaiga (Karnataka) all host nuclear power stations, but each of these was built later, after Tarapur had already started generating power.
Final Answer:
Tarapur was the site of India's first nuclear power station.\[ \boxed{\text{Tarapur}} \]