>>>>Thank you for the tip , I will look at pulaski road. May be some store owner near syosset station will agree to host my bike ...for some nominal fee<<<<
I'm a little unclear as to what your goal is. If you're going to take the train most of the way in, why not just ride from Northport to Huntington Station? It's the same line as Syosset and it's a direct run into Manhattan. You won't even save any money riding the two additional stops to Syosset because it's in the same zone as Huntington.
If the ride from Northport to Syosset is all you need to get your day off to a happy start, I understand. That's longer than my entire daily commute. Otherwise, I think you may find this whole ordeal to be a bit of a hassle. Riding from Syosset to Manhattan is something I've done for fun a few times, but I wouldn't enjoy it as a daily - or even weekly - ritual. There's no safe, peaceful, or scenic route, as I suspect you had from Riverdale.
I don't want to discourage you. What, exactly, do you want from whichever option you choose?