I don't know where you are located in Ohio, but you might want to take Rt 23 south until it turns into I-26. It's all 4-lane highway, mostly limited access. It is hilly, but you have to get across all the mountains to get to the ocean, no matter which way you go.
If you do travel this way, take the bypass around Ashland, KY; but head straight down, then it's a straight shot to the TN border, where it turns into I-26. Down through NC and then SC until you intersect I-95. Another 60 miles or so on I-95 until you exit into Beaufort.