For the most part, there really are limited dining options in Norwich, and most people in search of food will head into New Hampshire (less imposing than it sounds, as Hanover is just over the bridge).  That said, there are actually a few great options for those in search of food.

All the options are within a quarter mile of the village green downtown, and I don't think there are any other Norwich dining establishments outside of this little area.

Award winning chef Peter Ireland is in charge of Carpender and Main, an upscale restaurant that changes their menu seasonally.  A relatively small place, Carpender and Main has been featured in Boston Magazine's "Best of New England" edition.

Right across the street from Carpender and Main is the Norwich Inn, which actually has two separate dining options.  The Jasper Murdock pub is a little more low key, and offers outdoor dining during the summer.  In the main dining hall of the inn is the more upscale and formal eating, and the menu/price reflects this.

Next to the Norwich Inn is Dan and Whits general store.  Not really a dining establishment per se, but don't leave down without having a McWhit in the morning.  Regardless of the dining, this place is really a must see in Vermont, as it is the epitome of Vermont Country store - the slogan "If we don't have it, you don't need it" truly applies here.