Kew Gardens Cab (technically a "car service" not a taxi) was $18 a few months ago. They pick up at the airport, or your crash pad.
718-846-6666

Debora Cab, car service like Kew Gardens, about the same pricing.
718-803-1920

Ester at JFK Car Service was highly recommended by another crew member, but never used them personally.
347-803-9818

The Kew Runner has regular service between both LGA/JFK and Kew Gardens, run by Kew Gardens cab, but slightly cheaper. To get from airport to airport, you will have to change cars in Kew Gardens.
718-846-4900.

Every time I compared prices, Lyft was cheaper than Uber, by quite a bit.

Just be glad you don't have to do EWR.