From Alibag, you will need someone who can take you to the Elijah Rock by car. It is off of a sideroad and not easily accessible unless you have a driver who knows where to find it.
To visit the Elijah Rock, you need to travel to Alibag (also spelled Alibaug). Alibag is a three-hour drive from Mumbai, but is also accessible most of the year via catmaran. The catmaran (the fare each way is about $2.50.) travels between the Gateway of India and Mandwa Jetty and takes about an hour.