With all those suitcases, UberXL or one of the shuttle services such as SuperShuttle are really your best option. There is a bus to Grand Central (I forget the name but you can't miss it when you walk outside the AA terminal as there are signs and they are selling tickets) but you'll still be a few blocks from the Marriotts in Midtown Manhattan and schlepping suitcases through the city with a 2 y/o will color your marital bliss for the next three weeks!

I'd think about the Brooklyn Bridge, the Midtown Renn, or one of the Marriotts in Midtown. All have plenty of things to do for the day before you head back to JFK the next morning. The BB and the Midtown Renn will be slightly quicker trips.