There is more frequent service on the LIRR from Jamaica to Penn Station than there is on NJ Transit from Newark Airport Rail Station to Penn Station.

There is express bus service from all three NYC-area airports (not just from EWR) to mid-town Manhattan. And, for door-to-door service, there is also Super Shuttle.

If the OP's sister elects to fly into JFK and ride the "E" train subway into Manhattan, she should exit to the rear of the train when it arrives at Lexington Avenue/53rd Street. There is an exit from the station onto Third Avenue and 53rd Street, just three blocks from here intended destination.