I live in Bear DE. In my opinion the 3 best public courses (also some of the more expensive) in this area are Golf Club at Glen Mills (Glen Mills, PA), White Clay Creek (Christina, DE), and Bulle Rocke (Havre de Grace, MD). If you stay somewhere in Wilmington you are 20-30 minutes from Glen Mills and Bulle Rocke and 5-10 minutes from White Clay. White Clay is still recovering from the hurricane and was closed for about 2 months. I just played there thursday and it's like the greens haven't been touched. I am somewhat biased b/c I'm a member there, but I'm sure anyone on this board who's played there would say I'm not too far off in my opinions.
If you're looking for golf on the cheap. Inniscrone (Avondale PA) (this is a love it or hate it course, I love it for $40), Rock Manor (Wilmington, DE) (5 hour round), and Running Deer (Elmer, NJ $55, tough course needs money put into it).