Hello,
I am originally from Rhode Island and now live in Savannah, GA, (a half hour from Hilton Head). I have done the drive or flown back and forth to RI over the last 10 years. Sometimes the ride is quick and sometimes we have hit terrible traffic on the 95 corridor. At those times I wish we had flown. But not having to deal with airports, changing planes, and having our own car are all a plus. I guess it depends on your tolerance for long rides and possible traffic.
If you drive, the most important thing is to plan when you will drive through NY, Baltimore and Washington, DC. If you can avoid morning or evening rush hour do so. If you can drive through those cities on a Sat or Sun early in the morning, even better. Our son drives straight though overnight when he visits. (We stop part way) Two weeks ago he left Savannah at 4PM on Sat afternoon and arrived home in RI at 8AM Sunday morning. Got right though the big cities very early on a Sun morning and had no traffic or construction.
You will love Disney's Hilton Head Island Resort. Even though we live so close, we have stayed there more than once on points. The island is made for bike riding and there is so much to do.