"Take a bike path on Ocean Parkway (West side) in Brooklyn, make a left on Neptune Ave. (half a mile before an ocean), cross Coney Island Ave., ride on Emmons Ave. along an inlet (people over there call it a channel).
Or ride the Ocean Parkway bike path all the way to the ocean, make a left on Brighton Beach Ave. or a boardwalk (bikes are allowed on the boardwalk during some specific hours but people ride there all the day), ride through Russian ""Little Odessa""; at the end make a left to the ""channel"" (its _North_ side). In about half a mile after the channel watch for a bike path entrance on the right (before an entrance on Shore Pkwy).
Ride to Flatbush Ave., make a right, go over a bridge (West side), make a left and ride to Far Rockaway. (Also you can take Cross Bay Blvd. to Rockaway or take A train to Far Rockaway). Then take Seagirt Ave., at the end make a right over a bridge and you are on Long Beach.
I think it's about 27 miles from City Hall. Then it's about 10 miles to Lido Beach (I guess this is a place you want to go to). There is the LIRR station over there.
Have a nice ride."

I just looked at the map again. The route is about 25 miles from the beginning of the Ocean Parkway and about 32 miles from City Hall. You'll need to stop a few times on the Ocean Parkway part of the route down to the channel (it's about 6-7 miles) and (as far as I remember) a few times on the next 18-20 miles.
I don't like clipping in while riding in the city, so I have the SPD pedals with one side flat and the shoes look like sneakers. So I don't have a problem of choice before the ride :)
I think you can ride from City Hall to Lido Beach in 2.5 hours.