Elephanta is an island off the Mumbai (Bombay) coast. So the first point is to get to Mumbai city. This is one of the most connected cities in India.
A large number of daily flights are operated to Mumbai (BOM) from the rest of the main cities in India. So are the international connections to Mumbai.
Both are terminal stations, so it is a bit easy to get out and get in. By the way CST (Chhatrapati Shivaji Terminus) railway station itself is a UNESCO World Heritage Site.
Despite the noisy crowd you may encounter inside main cave in Elephanta , this image of Lord Shiva with his closed eyelids and in a deep contemplating attitude would be the most satisfying piece of art you would ever see in India.Rather this is the highest watermark of medieval Indian art tradition.