Dover (the capital) is centrally located if you want to take in both the southern and northern parts of the state. It's a small city and both the beach (Rehoboth Beach is the big beach town) and the more historical sites in the northern part of the state are accessible within 90 minutes. Wilmington (north) is the largest city in the state. New Castle is a charming colonial town with good restaurants, and the "Route 52" area between Wilmington and the PA border has nice restaurants and shopping.. If you enjoy American history and furniture, Winterthur is a must-see. Longwood Gardens just over the border in PA is also a must-see. The Hagley Museum gives the history of the DuPont company. Ashland Nature Center northwest of Wilmington has nice walking trails.
I lived in the northern area twice for a total of more than 15 years, but haven't spent much time there since we moved away in 1995 so you'll need specific restaurant recommendations from others.
Hope this is useful and have a wonderful trip!