When I fly from JFK, I park on the street for free near the Lefferts Blvd Airtrain station. The Airtrain is free from this location to the airport.

When I arrived at JFK last night, just for fun I checked the uber and Lyft app to check pricing to Westchester from the Delta terminal. I was surprised to see uber and Lyft were both about the same price $115. I usually find Lyft cheaper.

When I exited the Lefferts Blvd Airtrain station, I checked both apps. Lyft was roughly $115, but Uber was $80. That extra 10 minute ride to Lefferts was $35 cheaper. Something to think about.
I know prices vary, but a $35 difference was a big discount. Will it be the same for visitors heading to Manhattan? Who knows. YMMV.

dh