If you only have a few days and are starting in New York City, I might suggest following US 1, a highway which goes from Maine to Florida Where available, you can choose to take US 1A (also known as Alternate US 1 - it's not a contiguous highway) for a more scenic coastal route. From New York, you can head north into New England (cool days, chilly nights in April). Or, for warm weather, head south from New York along the Mid-Atlantic coast into the South and all the way to Key West, if time permits.
Some of the best American regional cuisine is located along the East Coast. Most of the seasonal diners, crab shacks and lobster pounds will be open by April, but not yet crowded. My personal favorites include: the Maine Diner in Wells, Maine; Essex Seafood in Essex, Massachusetts; Durgin Park in Boston, Massachusetts; Mrs. Wilke's Dining Room in Savannah, Georgia; the Dixie Crossroads in Titusville, Florida; and Wolfie Cohen's Rascal House in Miami Beach, Florida. There are simply too many to list; you need to get the Roadfood book or see their website. Happy travels and happy eating.