I'm not free this coming week, but wanted to get my post in here as another Wilmington mama (mom to be!)
I second Hugh McRae park. Its nice - kids like the pond (bring bread, there are tons of big turtles in the pond that come out for the food!)
You could also head down to Wrightsville Beach Park, it's the start of the walking "loop" that will walk you over the intercoastal and through the small town of Wrightsville Beach - very pretty. There is a small playground in that park as well.
Both have websites, I think.