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Given how many legs the public transit route would require, I’d go for an Uber.
I did the subway/LIRR/airtrain from the Upper East Side to JFK in June and still paid $16.50 (and took a good 75 minutes) – with four of you, doesn’t sound like much savings for all the hassle.
For reference, my Uber back (at 10pm) was $91, including tip and tolls.
Rental car doesn’t sound worth it to me either.