Call Queens Village car service the cost is approximately $22.50 before tip. They have coupons you can print on their web site. The phone number is 718-776-8787. This is your best and most reliable option. I will be using them this weekend for a commute from Jamaica Station to LaGuardia.
From JFK, take the "Air Train" to Jamaica Station. There, you can catch the LIRR (Long Island Railroad) into Penn Station in Manhattan. From Penn Station, you can catch an Amtrak train upstate to Albany.
Take the Long Island Railroad to Jamaica and change for a train going to Valley Stream. If you are not near the LIRR, take the E or J subway train to the Jamaica LIRR station and change to the railroad there. The only train that stops in Jamaica is the LIRR. The subway does not go into Nassau County.
Hewlett - LIRR station - was created in 1869.
Oakdale - LIRR station - was created in 1868.
Pineaire - LIRR station - ended in 1986.
Pineaire - LIRR station - was created in 1915.
Grumman - LIRR station - was created in 1942.
Bayport - LIRR station - was created in 1869.
Quogue - LIRR station - ended in 1998.
Quogue - LIRR station - was created in 1875.
Hillside - LIRR station - was created in 1890.
Hillside - LIRR station - ended in 1966.