If you have time for a picnic in a park I definitely would recommend Roundhay Park. It is a huge park with two ponds - great for bird watching, wildlife and butterflies observations in the summertime. Lots of walking paths, some in the shady areas some in the sun, so depending on the weather you can pick and choose where to walk. Bring a picnic for your family; there is a cafe in the park so you can buy lunch there but options are somewhat limited. This park also has a mansion and several playgrounds for kids. Seems like a perfect place for the family outing.