Now, I don't know the area of Long Beach all that well, but with the help of Mapquest, I have found 2 routings to bring the LIRR to Jones Beach.
From Long Beach RR, continue south to near the shore, then run it along the shoreline(not right at the shore, behind the beach, but south of where the houses are), then over the inlet to Jones Beach
or
From Long Beach RR station, there is Park Av. Park Av has a median. Run the trains down the median(above grade) to where it becomes Lido Blvd(no median). I'm not sure about that area, but I'm sure something can be found. It's only about 1 mile that I'm unsure of. That is the section between Park Av and Lido Beach West Town Park(which may be even less than a mile). From there, 2 options:
1. North of Lido Blvd, between Lido Blvd and the Golf Club, then crosses onto the south side of Lido Blvd, dives southeast through Point Lookout town park, then across the inlet to Jones Beach.
2. Southeast through Lido Beach West Town Park, east through Lido Beach District Park, Lido Beach Town Park, Nassau Beach County Park, Point Lookout Town Park, across the inlet to Jones Beach
After crossing the inlet, there's an array of possible ROWs. One could be down the median of Bay Pkwy, then Ocean Pkwy, with stops at some place on the beach and then maybe another one at the amphitheatre
I think option 2 would be the best, but I still need to visit the area and check out just how clear the possible ROW is. Where was the original one?