Wilmington — Just 15 minutes by Amtrak, Delaware's largest city punches above its weight culturally. The Brandywine Valley museums (including the outstanding Brandywine River Museum of Art with its Wyeth collections) and the Hagley Museum — set on the original du Pont gunpowder mills — are both within easy reach. A half-day is enough for a focused visit.
Philadelphia — 45 minutes by Amtrak on the Northeast Corridor, Philadelphia is the obvious big-city excursion. The historic district, Reading Terminal Market, the Philadelphia Museum of Art, and the vibrant restaurant scene give you more than enough for a full day.
Longwood Gardens — About 30 minutes by car into Kennett Square, Pennsylvania, Longwood Gardens is one of the great botanical gardens of North America. Stunning in any season, with particularly impressive glasshouse displays in winter and spectacular outdoor gardens from spring through fall.
Chesapeake and Delaware Canal — Around 30 minutes south of Newark, this historic waterway cuts across the Delmarva Peninsula connecting the two bays. The area around the canal is scenic and good for a quiet drive or a walk along the towpath, with views of the working commercial traffic that still uses the canal today.