The Atlantic Flyway and the Appalachian Trail
While it is true that there are many resort towns on the Atlantic Coast that cater to the Spring Break crowd, there are even more National Wildlife Refuges that offer the chance to experience the barrier island coast the way it has existed for millennia. I think that taking a leisurely drive down the coast (as opposed to using I-95) and visiting a number of those venues might be pretty close to what you have in mind. Try heading for the Chesapeake Bay the first day and then wandering down the Delmarva Peninsula (Bombay Hook, Assateague, Chincoteague, and others), then visit the Outer Banks of North Carolina (Cape Hatteras National Seashore) with a final target of say Cumberland Island National Seashore in Georgia, and I think you'll find a much quieter version of the Atlantic Coast than Myrtle or Daytona Beaches. On the way home you can work your way north along the Piedmont Plateau just east of the Appalachian Mountains (roughly paralleling the Appalachian Trail or using I-81). There are a ton of National Forests along here that offer the opportunity to do some hiking and the views (with the leaves off the trees) should be spectacular.
AZBuck