BOM
 

We will reach Mumbai Airport at 0815 hrs and our connection flight to Kolkata is at 1830 Hrs. Kindly advice how to spent time. We are 2 adult and a child with three luggages.

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you could probably store your luggage and then head out to the Juhu Beach area for street food, shopping, walking on the beach etc. If memory serves me correct, the JW Marriott Juhu Beach has a day pass you can buy for their spa and lounge which I would highly recommend as I think they have child minders and pools you can use.
I would NOT recommend you head down to Colaba or the old town district as traffic there and back will take most of the time out of your day. The mumbai airport is nice and I would try to pay for lounge access if they allow it, but probably not with a child in tow as it could get boring for them.

Don't forget your transit visas to leave the airport!

is this an international-domestic or domestic-domestic connection????also, which airline are you flying & have you tried to check your luggage in to your final destination????