Dover is a TINY (population 425), poor town with, I'm certain, nothing at all for a teenager to do.
Here is the City-Data page on Dover with some info. I presume that if your grandparents are there, you have been before and seen it, but you need to think (all presuming it is OK with your parents and granparents, of course, since you are still a minor) about what your day-to-day life would be there. You'd be the "new kid" among a lot of folks who've lived there and known each other their whole lives. You'd probably have to go into Kinston for any "teen activities", and Kinston ain't all that anymore. Most folks your age are getting out of these little towns as fast as they can't, not moving IN to them, but if you think your quality of life would be better, and it works out, maybe it would be an improvement.
Are you talking about moving in the middle of a school year? That will bring extra problems. And if you're looking at college, would you want to go to a VA or NC school? If you move to NC, you will probably lose in-state residency in Virginia, which could affect admissions and cost (though it would also positively affect the same for NC, once you had lived here a year).
Basically, you are still a minor and nobody can really "advise" you since your parents have the trump card on most aspects of your life right now.