Helicopter Flight Training out at Islip does have R44s (
www.helicopterflighttraininginc.com). Not sure if their B206 is finished yet. They might be able to help.
The Long Island Railroad has a stop nearby the airport (Ronkonkoma), and you can walk to their location in 10-15 mins. It is about 50 miles from Manhattan though, and to get to Manhattan, a transit through JFK/LGA class B is required.
Pegasus in Linden might also be able to help (
www.pegasusflight.com). Their website does show a R44 for tours. Getting there might be challenging. There is a NJ Transit station in Linden but I'm not sure how far from the airport it is.
All the best. Hope you can find what you're looking for.