This will be a fun exercise...
MA: Barnstable, Berkshire, Bristol, Dukes, Essex, Franklin, Hampden, Hampshire, Middlesex, Nantucket, Norfolk, Plymouth, Suffolk, Worcester
NH: Belknap, Carroll, Cheshire, Coos, Grafton, Hillsborough, Merrimack, Rockingham, Strafford, Sullivan
ME: York (close on a couple others though)
VT: Windham, Bennington, Windsor, Addison, Washington, Essex (only missing 1 road in both Rutland and Orange)
RI: Bristol, Newport (very close on Washington and Kent)
NY: Richmond
VA: Virginia Beach, Suffolk, Isle of Wight, Hampton, Newport News, Poquoson, York, James City, Williamsburg, Manassas Park (only missing 1 road in Norfolk, Charles City, Hopewell, Manassas; very close in Chesapeake, Portsmouth, Gloucester, Fairfax (city))
NC: (Currituck would be here if not for NC 136)
MA raises an interesting question though - two of those counties don't contain any numbered highways. I'm counting them here (in italics) even though I've never been to either county, because 100% of 0 is still 0.