I'm from Newport moved to NH 24 years ago, I go back several times a year with NH plates, in fact going next weekend. Its a great ride and a great place to ride around. I never had a problem and still don't to this day. If your not trying to draw attention to yourself no one bothers you.
Its just like any small tourist town, when there are that many people on foot and people hanging out at the shops window shopping which by the way are right on the street or hanging out at the beach, they don't want loud bikes disturbing the peace of those spending money at the shops. Every little sea side town is like that. Even the ones off the coast in MA and Maine. Just keep the decibels down and no one looks twice at you.
Mark