Originally Posted by
Petdog
AirTrain in the other direction, to Howard Beach.
A train to Inwood not the Rockaways.
At Jay Street (in Brooklyn), switch to the F train to Jamaica/179 St.
Get off at Delancey/Essex and walk east to Holiday Inn.
That will bring the cost for two to $21.
Instead, I'd recommend taking the Q10 or Q10 Limited from JFK T5 to Lefferts Boulevard and Jamaica Avenue. Walk about 500 feet East on Jamaica Avenue to the 121st Street (elevated) subway station. Take any Manhattan-bound train to Essex and Delaney. Total cost for two: $5.50, with free transfer from bus to subway, if paying with a MetroCard, or a contactless credit/debit card.
Note: There is no elevator or escalator at 121st Street station. If the OP and companion just have carry-on luggage that is not too heavy, they should be OK. Otherwise, they can get off the bus at Lefferts and Liberty Avenue, and take a Manhattan-bound A train to Jay Street, Brooklyn, and transfer there to a Manhattan/Queens-bound F, as suggested. (Lefferts Boulevard station has an elevator.)
If the OP is not arriving at JFK T5, the AirTrain can be taken -- without charge -- from any terminal to T5.