Elephanta Island, situated in Mumbai Harbour off the coast of Maharashtra, is the UNESCO World Heritage Site famous for its ancient rock-cut caves and sculptures, so it is the correct answer.

Locally the island is called Gharapuri ("city of caves"); the Portuguese named it Elephanta after a large stone elephant statue they found there. The island houses a group of cave temples carved out of solid basalt rock, chiefly dedicated to Lord Shiva. The masterpiece is the colossal three-headed bust known as the Trimurti (also called Sadashiva/Maheshamurti), which depicts the creative, preserving and destructive aspects of Shiva. These sculptures are generally attributed to roughly the 5th–8th centuries CE, and the site was inscribed on the UNESCO World Heritage List in 1987.

The other islands do not fit the description:

• Salsette Island is the large island on which much of Mumbai and Thane city stand; it is not primarily known as a cave heritage site.
• Khanderi Island is a small fortified island associated with Maratha naval history, not ancient caves.
• Butcher Island is used mainly as an oil-storage and port facility in Mumbai Harbour.