Plenty to do & see. Go for a car ride, canoe, or bike ride, through beautiful BeaverValley Creek off 202. Visit Concord Mall or the Brandywine shopping center for tax free shipping. See the Hagley Museum. Much more too.
My home, so I'd better love it - for a traveller, I'd think Wilmington would be an ideal place to set down roots for a stay of a week or more, with the intention of driving to the larger cities and beautiful small town and country spots nearby. Wilmington is legitimately in the middle of it all - as a midpoint between New York City and Washington, DC, with plenty of its own charms as a pretty little city, has a lot to offer a traveller looking for a less conventional basecamp.
Delaware and especially Wilmington is known as the home of the corporation but not much else.
Wilmington is known for corporations and for it's nightlife. It has a port, several nice colonial neighborhoods and, at Trolley Square, several popular local bars.