Starting at the New Castle Farmer's Market on Rt 14 in New Castle, DE (which is also a neat place to walk around, inside and out), leave the Market and head East on Rt 72 (runs along the side of Market). This will bring you into Old New Castle. Left (south) onto Rt 9 (Rt 9 is clearly marked at turns).
You can follow this all the way to below the Dover Air Force Base. You will go through Old New Castle, Port Penn, Reedy Point Bridge over the C&D canal, Augustine Beach (nice stop just to take a break, site of former Augustine Inn now closed). Small beach area there with port-a-potties, fishing, picnic tables.
Heading south takes you through beautiful marshlands, wildlife areas, nice road, little traffic. When you get to Rt6 you can turn left and also head a few miles east to Woodland Beach. Rt 9 ends just below DAFB, joins up with Rt 113