Do new restaurants pop up in Stanford very often?

It wouldn't appear as such. There are definitely restaurants operating in Stanford but there just aren't a ton, and a big reason why is the size of the town (a couple thousand people at most) -- the market is pretty small. If there's anywhere in Dutchess County where I know for a fact that new restaurants pop up at a better clip, it's the southwestern part from maybe Hyde Park down to Beacon.