Have a picnic or see a historic DuPont mansion
Bellevue State Park is a historic natural park just outside of Wilmington, Delaware. The park is built on grounds once owned by Delaware's famous DuPont family and makes for a perfect mixture of nature and culture. Sure, you can come and take a walk, have a picnic, play tennis, or ride horses in the Wellspring Stables, but you can also tour the historic estate of William DuPont: Bellevue Hall.
Bellevue Hall is an impression mansion and the personal pet project of William DuPont. They hold regular tours of the mansions and, honestly, it's a worthwhile thing to consider given DuPont's importance in the state. As far as trails go, there are two main ones you should keep an eye out for: The Brandywine River Trail and the Nature Preserve Trail. The former is the easiest trail and takes you along the banks of the scenic Brandywine River while the latter takes you through the Bellevue Woods Nature Preserve. Both begin near the entrance to the park.