I live near Atlanta, and we vacation in HH all of the time. The drive down takes about 5 hours with a little one in tow, but you can do it in 4 without kids. I, personally, wouldn't want to do it that way. Depending on where you are coming from, fly into ATL, then catch a separate flight from Airtran to SAV. The Airtran flights go on sale frequently for $49 (sometimes even $29, but those are rare) one way, and are often available for $69 or $79. This may be a more attractive offer than the long drive. Don't forget to factor in gas and food on the road when comparing the prices.
Disney's HHI is a wonderful resort, though it is not located directly on the beach or a golf course. They do have a shuttle that takes you to the beach, and it is a little nicer than some of the beaches on the plantations.
Personally, I prefer Disney's VB resort. A stay there in May is actually what triggered my wife to want to buy into
DVC. The resort is not located in Vero Beach proper, but it is on a very nice stretch of A1A just outside of Vero. The golf (again off-site) is nothing like the golfing at HH, but there are some very nice courses in the general vicinity. The beach blows HH away. The resort is right on the ocean with direct beach access. The pool is nicer at Vero as well. I think Vero is my Disney favorite resort. If only they could figure a way to get that beach to Orlando!
A lot of people fly into MCO or MLB for Vero. Orlando is a full two hours away, and Melbourne is about 50 minutes away. I personally prefer to fly into PBI. West Palm is only about 1 hour and 15 minutes away, but the airport and car rental facility is easier to get into and out of at PBI, and it is cheaper than MLB. Rates for PBI are usually a little higher than MCO by about $10/leg for a one-way ticket. I think the time saved and convenience are worth the expense.