By "unstructured" I meant allow for the basic template of each park to be a flat grassy lawn, with no (or very few, around the edges maybe) gardens. The sidewalks are all that are needed to service the parks, and maybe for the larger parcels, a single bisecting sidewalk. Have the walks follow the same street grid that works rather than trying to mimic some woodsy trail.
I tried to find an example of one for about 5 minutes, and I couldn't. A park the size of a block, with wide sidewalks around and a bisecting walk through the center (perhaps a fountain or sculpture of some sort as a focal point). The rest would simply be a lawn, with a few benches and lamps to allow use at night. Sidewalks would be wide enough for street vendors to sell their wares. I can see this as the most successful, because people can come to do whatever they please. In a city, where most people don't (and shouldn't) have yards, this would serve as a communal front lawn. How many yards have you seen in the suburbs where kids play catch, while leaping over patches of dead flowers and mulch?