Just spent several days in Newport, and although all of my dinners were corporate catered events at the Hyatt, I can tell you that the dining in Newport is, for the most part, very casual. I'd be prepared for the white pants, sweater-over-the-shoulders type of dinner outfits.
Most of the restaurants I saw in the downtown area were either pub-types or seafood places, none of which looked formal. If you are eating in a more upscale hotel, you might dress up more, but from what I saw, everything was very casual.
Just FYI, the downtown area has a Panera Bread shop, Starbucks and a Subway for your casual eating pleasure
(When I refer to downtown, I am referring to the waterfront/tourist area at the harbor/docks.....if you are staying more inland in Newport proper, you will have other food choices than those I mentioned.)