Suggested route across Long Island?
I live in Astoria and bike over the Queensboro bridge to work in Manhattan, and back, every weekday. I've also biked all over the general area. Personally, I would not take Queens Boulevard. It's mostly a four-lane situation, and is not pleasant for cycling. It's complex and constantly changing situation that will have you going quite slow to watch out for cars coming from every which way. Not to mention some cars park paralell, and some in other directions. You have to watch for doors, and also getting backed into. If you have to cross from one side to the other at any point, good luck. I had to do that a few times when biking to Maspeth, and I just gave up and walked it at a crosswalk. 

Bethpage is really far considering you are all the way in NJ. Biking in in the morning and using some other mode of transportation to get home is a good idea. Going both ways every day would be too much for most people. 

I would suggest listening to Google Maps. Their cycling directions have done well for me, and the path it charts from 59th street to Bethpage looks good. You have to remember complicated directions, but the tradeoff is you avoid really complicated traffic patterns and traffic itself. You'll also avoid lots of traffic lights making you stop all the time.

Maybe I'll see you on the bridge. Good luck.