Visiting the statue of Liberty

A few other public transit routes you could take that might be easier:

1. Walk to Jamaica Canter, take the J to Broad St. (about 55 minutes), walk 10-15 minutes through the heart of Wall Street to the ferry terminal/security screening in Battery Park. Cost: 1 subway ride. Google calls this 1:15 door-to-door.

2. Walk to Jamaica Station, board a Long Island Rail Road train for Atlantic Terminal (lookup schedules here, 20 minute ride). Transfer to the 5 (NYC subway) and exit at Bowling Green (8 minutes). Walk into Battery Park for the ferry. Cost: 1 subway ride + 1 LIRR ride. Google calls this 50 minutes door-to-door.

Option #2 will save you 25 minutes or so and is less walking, but at the cost of adding an LIRR fare and the inconvenience of a transfer. Up to you whether that makes sense.

You must, as Andrew Lazarus notes, get tickets in advance and will need to leave the hotel substantially before 4pm to arrive on time, even if you're on the last boat.

Your motel is near JFK airport, and not convenient to tourist attractions. However, you are very close to the subway station for the E train, which goes into Manhattan with very few stops.

I'm not a subway expert (but here is the map), but I would suggest taking the E to the Lexington/53rd station, transferring to a Lexington Avenue Local (6) southbound for one stop to Grand Central, and changing there to the Lexington Ave Express (5) bound for Bowling Green. Bowling Green is near the ferry terminal for the Statue of Liberty. The transfer at 53rd involves a rather lengthy enclosed corridor: when first built, these stations did not connect and did not offer free transfer. My recollection is that the change at Grand Central is from one side of the platform to the other.

Tickets for the ferry to the Statue of Liberty and Ellis Island are available in advance and do sell out.