Springfield and Bellows Falls are both nearby and each have a handful of options. I've heard good things about Miss Bellows Falls Diner, but haven't been yet.
I'm not sure how far out of the way you want to go but there is a great outdoor BBQ place at Exit 4 in Putney. It's called Curtis' and it's just off the exit (going towards Putney)
Curtis' restaurant is also on the same rte as the Vermont Country Store. The restaurant is closer to Chester. I've heard that the restaurant doesn't have the dry meat issues that the outdoor location in Putney has.