halfway points
Need to give a specific point in NC... it's a pretty substantially sized state, after all, and the distance from, say, Rocky Mount will be significantly different than it will be from Charlotte, as will the halfway point.
Rochelle, Virginia is halfway between State College & Raleigh
North Dakota and South Dakota are about halfway.
Pennsylvania
NM
Mississippi
Tennessee
Kansas
Tennessee
No, but Sacramento is the state capital of the golden state, California.
Denver, Colorado is about halfway.