If you go down to Assateague you can keep riding on 611 to a nice little dead end on the back bay. Used to be a little picnic area right on the water, not sure if it is still there. If you want to go north you can take Rt. 1 up to Cape Henlopen State Park. Time permitting you can take the ferry across the bay to Cape May, NJ. Don't know if it has changed but Delaware had a no helmet law a while back. Took my chances and rode w/o the helmet for a bit and loved it. Be careful on the coastal highway in OC, also known as the 8 lanes of death. Lots of pedestrians and tourists looking everywhere but the road. There are some really nice back roads with wide open farm land if you're in to that. Hoopers is pretty good as is Philips. You could also check out BJ's on The Water, Fagers Island and Harrison's Harbor Watch is nice, right on the inlet. If you want to check out the other boardwalks (a little less crowded) you can head up Rt. 1 to Bethany or Rehobeth Beach.
Been a while since I've lived there but give a shout if you have any other questions.
Enjoy it, I have some great memories of the shore there!
Forgot about the Salisbury Zoo. Really nice little zoo conisdering it is the Eastern Shore and it is Salisbury. Right off of Rt. 50 if you don't take the bybass.