I was checking into this a few months back. Savannah, GA is the closest airport to HHI and Charleston, SC is a second option.
You can fly direct to Savannah from Philadelphia via US Air. Another option since you already use BWI is to fly SW to Charleston, SC. The Charleston, SC airport is approx 2 hours north of HHI but it may be more cost effective. I never looked into the train option.
We are planning to go around the Christmas holiday so we have some extra days allocated as travel time. I am still not crazy about the long drive so hope it will be worth it and that we don't kill each other on the drive. My husband and I always agree to disagree on the route to be taken when traveling anywhere.
There are other options flying/train and I am certain others will comment on this.
Good luck and have a great time!