"A nice motorbike route that hugs the coastline" sure covers a lot of ground--a couple of thousand road miles, much of which is heavily built up, overpopulated, clogged with traffic, and not even particularly scenic. You're more likely to gather useful suggestions if you limit your questions to one short section at a time, probably after doing your own research.
You might also want to define "hugging the coast," since that could have you wandering urban and suburban neighborhoods almost the entire length of, for example, Brooklyn, Queens and Long Island, or doing the same on the mainland side of Long Island Sound, or skirting the whole New York metropolitan megapolis in favor of the very pleasant backroads of New York and southern New England (my personal preference).
No matter how you do it, "hugging the coast" will involve a lot of stoplights and strip malls. I've covered most of the coast at various points during the past 50 years, and only bits and pieces are really worth your time and energy. Even stuff that's fun to experience tends to get decidedly old after a while (c.f. Rt. 1 in Florida)--that's what interstate highways are for.
Don't know if that's helpful, but I hope it's a start.
Mark
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