About the most annoying area to ride in, in Nassau, is between Garden City and east of Hicksville. There isn't a road or route I'd recommend while trying to go west to east.

Thus I'd suggest heading up to the LIE service road at some point (Little Neck Parkway is my preference) and just head east. Yes you will hit some hills, but I ride the hills as preference then trying to find my way thru Westbury and Hicksville.

The LIE service road ends at Woodbury Rd. If you don't want to bike path at that point, head up Sunnyside Lane, it's a bit more gradual then the path, hang a right over the NSP and LIE and make a left on Executive Drive and over to Washington. Again, some hills but better then the congested alternatives.

As well and FWIW, my east/west south shore route is to avoid Merrick and take the following from the Bike Path. Clark, Park, Old Mill, Wilson, Grand-Smith, Babylon Tpk., Seaman, Lakeview, Franklin, Dutch Plains. That gets you into Queens from the east. This is also the route of the Ride to Montauk as well as Montauk Century's.