Some of the NY specialties to try while they are here are:
Bagel w/lox
Egg cream (no eggs are involved)
NY Pizza
NY delicatessen sandwiches
Italian ices, pastries, cannoli
all the ethnic foods you find in NYC and many more I'm overlooking.
Speaking of hole-in-the-wall places…
Il Laboratorio Del Gelato on Orchard St. between Broome and Delancey Sts. makes their ice cream by hand in the back and they have some specialty flavors.
For Jenny's Dim Sum try the Double Eight Palace for brunch at 88 East Broadway underneath the Manhattan Bridge.
I have to think about transportation to Jones Beach.
The easiest route is by car - LI is all about cars - (midtown tunnel-LIE east, to Cross Island Pkwy south, to Southern Sate Pkwy east, to Meadowbrook State Pkwy south).
{edit}
I looked up a couple of ways to take the train to the beaches.
- The LIRR from Penn Station has a Far Rockaway stop at the beach there. (I haven't been to the beach there)
- For Jones Beach take the LIRR to Wantagh then take the JB24 or JB50 buses to the beach.
Coney Island might be an easier choice. There are a couple of subway stops there and at the nearby aquarium. I haven't been to the beach there (other than driving by) in quite a while.