Breakfast in Hanover NH
In downtown Hanover (5 minutes from DHMC) is Lou's. Lou's is THE place for breakfast in Hanover. It's a diner type atmosphere, but a bit more upscale. Lou's has been around since the '40's and is only open for breakfast and lunch. Just fyi, DHMC's cafeteria is not bad, especially for breakfast.
I would add a vote for the Fort, just off I-93 in Lebanon. Superior, homey diner food -- clearly a draw for locals and truckers alike. I had outstanding corned beef hash and sincerely regret I do not live in the area -- the banana walnut pancakes deserve a return visit, for sure. Great waitstaff, too.
For good diner type food, there is the Fort in Lebanon or Lous in Hanover.
If you'd like to sit for something a bit nicer we like the Norwich Inn across the river in VT or Market Table in downtown Hanover.
DHMC is a great facility. Good luck!
Norwich Inn Restaurant
325 Main Street, Norwich, VT