We've driven from Central MA to WDW with our four kids four times, starting when they were all quite small. The gas prices varied, but I'd say our minivans probably went thru $150 - $200 worth of gas each time. We'd spend two nites in hotels going down and coming back, so that added to the cost of the trip, too, but it was still cheaper than air fare.
We'd leave late at nite so the kids would sleep for the first eight or so hours of the trip. When they started to wake up, we'd just about be in Washington, DC, where we'd stop for breakfast and tour the National Zoo. It's free, it's fun, and it gave everyone a nice stretch. Then back in the car. I packed a cooler, the kind you plug into the car outlet, with cold drinks and sandwiches. We'd stop for lunch at a rest area on the highway. The rest areas anywhere but Massachusetts are usually very nice! Then we'd continue until we just couldn't stand being in the car any more, usually around 3:00 or 3:30 in the afternoon. I'd refer to our Trip Tix from
AAA to find a hotel, call from the car for a reservation, and we'd stop for a swim, dinner, and a good nite's sleep. Day Two was pretty much straight driving, stopping only to eat another picnic lunch. We'd spend one more night at a hotel, then make it to Disney late the next morning.
The kids were responsible for their own car 'entertainment'. They'd have games, Walkmen, coloring books, whatever, and, of course, each other. Sometimes they'd entertain each other nicely, sometimes not so nicely. For those not-so-nicely times, I brought a book on tape. I'd put my headphones on and drown them out until they settled down

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Overall, driving down worked well for us and our kids. This summer, we plan to drive down again. Now that the kids are all teens, we'll probably only have our youngest with us. The thought of being in a car with a 15-year-old girl the entire length of the East Coast doesn't excite me too much. I think I'd rather travel with 2-year-olds!!! But the drive itself isn't bad, and it certainly saves $$$. However, I wouldn't go without AAA even with a new car. Stuff happens, flat tires, whatever, and the tour books they give you offer some good info about the places you're going thru.
Have a great trip. We always go in July or August, and the crowds can be bad, but we enjoy Disney anyways!