We're from the NYC area and we stayed at HH over the Thanksgiving Holiday. We researched airfares greatly as we have three airports to choose from (JFK, LGA & ISP (regional). We found in all cases that jacksonville (JAX) was cheaper to fly into and drive the 2.5 - 3 hr trip to HH than fly into any other airport including Atlanta and Charleston.
Also since you will need to rent a car to get around on HH, we found that rental car prices are considerbly less than the other locations by about half.
We had used a Disney Club discount (not available anymore) but I do believe
DVC (MS) offers discounts using Alamo for rental cars in Florida.
You'll also notice that there are usually more flight selections into JAX than the other airports.
Just a note. We flew USAir and when checking we did find that flights that had stops through Atlanta and then to JAX were still cheaper going onto JAX than just taking the same flight to Atlanta.
Atlanta is also 3-4 hrs in driving time. JAX is almost a direct drive up RT- I95 with speed limits posted up to 65mph.
Hope this helps.
We have used Savanah regional airport also and it is very nice and has good services and rental car facilities at the airport if you decide to fly into there.
Be advised that if you are using Expedia for your flight pricing that USAIR isn't allowing them to sell tickets until further notice. They are in a disagreement over some added chargers being added to flight costs by expedia on USAir flts only thus making their costs more money. Use Orbitz or another service to check your flt pricing.
Good Luck and shop wisely.
Kennyk