Johnny's Atlantic Beach
Most of your casual places, all in all I think most, not all will be open.
Are you looking for a place that has mostly seafood as in S&S?
If your looking for a late night snack and feel like pizza - Via Via on Thames delivers to your hotel. It is very good thin crust.
We spent the last 2 New Years in Newport and had very good meals at the following (all of which should be open):
Tucker's Bistro - on Broadway...eclectic creative cuisine
Pronto - Thames St. Very good Italian/International
Mama Luisa's - lower Thames St. Wonderful Northern Italian with an outstanding wine list.