Travelling by Air
Kerala has three main airports; in Cochin, Trivandrum and Calicut. All three airports are well connected with Mumbai and there are many direct flights between each of the airports through the day
Fly from Mumbai to Cochin if you are travelling to Fort Cochin, Munnar, Thekkady, Marari or Alleppey, Kumarakoam
If you are visiting Kovalam or Varkala it is closer to fly into Trivandrum from Mumbai
Wayanad, Kannur and Kasargod which are atthe northern most end of Kerala are closer to Calicut airport
Kochi Airport is serviced with the most number of flights from Mumbai. It means more flexibility on flight times and at times fares that are cheaper than that for flights to Calicut orTrivandrum.

Travelling by Rail
The southern India rail network known as Konkan railway runs a number of trains between Mumbai and Kerala
The major railway stations are Calicut, Ernakulam Junction (close to Fort Cochin) and Trivandrum central. There a few trains that also halt at Alleppey and Varkala stations
There are about 9-10 trains that run between Mumbai and Kerala. The average travel time is 16 to 24 hours, depending on the train and if you plan to alight in North/Central or South Kerala

Travelling by Road
The least recommended option is to travel from Mumbai to Kerala by road.

The distance from Mumbai to Cochin is 1377km
There are no direct buses that ply between the two regions.
Driving to Kerala with a rented car would mean a journey of two days with a night halt. (A care hire would be very expensive and not all car rental agencies would be willing to send a car and driver from Mumbai to Kerala)