Aside from Marikina River Park, do you know of other spots in Marikina (or near the city) that can be perfect for picnics and outdoor plays for kids?

Not in Marikina though, but the University of the Philippines is only a few kilometers away from the city. It is the best place if you want to set up picnic sheets and play with your kids. They also close a part of the oval every Sundays to give way to bikes and other activities.