Murphy's is just off the main green and has pretty solid food and a nice atmosphere. Apparently a number of Tuckies frequent the Canoe Club too, but you're probably best off letting people eat their meals in peace. Lou's is a popular breakfast spot right across the street from Murphy's and Molly's at the other end of downtown Hanover (all of two blocks) is another popular option for lunch or dinner.
As small as Hanover is, there are a plethora of dining options available, inclusing Thai, Chinese, Indian and Japanese restaurants. I've never been, but I think Yuri Yuri or Yami, or something like that, is supposed to have good sushi.
If you want to pick up some groceries, check out the Co-Op in Hanover or the one in Lebanon, near Dartmouth-Hitchcock Medical Center.
Have a great time in Hanover and best of luck with your interview at Tuck.