Since you'll be eating outside, pack nature-inspired foods like ants-on-a-log (celery or pretzel sticks with peanut butter and raisins), bug juice (fruit punch) and dirt cake (make a cake of your choice with chocolate frosting, sprinkle with crushed Oreos and gummy worms).
Many local parks play free movies outside on summer nights. Call ahead to the park offices for the summer film schedule, and ask what other organized events they're hosting. Many softball or soccer leagues play in local parks in the summer, and they'll always welcome cheering fans!
Bring a Frisbee or baseball and glove or play games that require no equipment at all like tag or red light green light.