I have done the drive from the Baltimore area at least 20 times in my life. Here are our three most often chosen options:
#1 - stop in southern Georgia somewhere - Richmond Hill is one of our favorites for price and options. Get there early enough to get a good dinner and to bed early. Hit the road at 5am so you get to the World at least close to park opening.
#2 - stop in Daytona or St. Augustine - this means that the first day of driving is VERY long, but it also means only 1-2 hours on the road in the morning before hitting Disney
#3 - Don't stop for the night. Trade drivers on a regular basis (if you can) stop at an assortment of rest areas between South Carolina and Disney for meal breaks/picnics and an hour or so of sleep at a time
Most people think that given the fact that we are now in our 40s and DD is 10, we would lean more toward option #1, but the truth is, the last 3 times we have done option #3 and been quite happy with it. We leave the Baltimore area some time mid/late morning (so we can be through DC/Nova before the worst of the traffic) and take 2 hour shifts driving with a couple of 1-2 hour stops to sleep in the car.
Why do we choose option #3? Cheapest. Rather use that $70-$100 at Disney than on a cheap hotel whose beds are rarely much more comfortable than a reclined car seat. DD can sleep anywhere any time and I can function quite well with very little sleep, so it works for us!
BTW - if you want more info/details, I keep a log of every drive (yup, that AR) and can give you lots of information - just message me.