.. the JFK AirTrain to Jamaica and transfer to the Long Island Rail Road.
There are two machines at Jamaica station (these two machines look different from all the others and they have green trim with railroad tracks alongside them). These machines sell combined JFK AirTrain / LIRR tickets (there is no $1.00 fee or anything). For off-peak travel (LIRR trains arriving Penn anytime after 10:00AM), the combined tickets are $12.00 USD per person (each way).
LIRR trains are much easier to connect to and are super frequent and very fast - they deliver you right into Midtown Manhattan (New York Penn Station opposite Macy's - one block from Herald Square - a five minute walk from Times Square) in less than 20 minutes. ..