The Batavia Quarry park when we were kids this was the place to go. it has a pool and off to one side there are big shaded areas with picnic tables, tennis courts etc.
wheeler park in geneva - big playground, mini golf, lots of paved trails and big grassy areas for running and playing. been going here for more than 50 years
phillips park in aurora is great. it has a big playground area, sunken garden, small zoo, train ride around the park (free) a fossil house (free) and reptile house (free) sprinkler park which runs all summer is also free. aquatic center is not free but is not super expensive either and it is great.
blackberry farms in aurora is great and across the street from that is the splash country water park
lincoln park in aurora over behind holy angels grade school is wonderful. nice playground, big paved trail for walking, picnic tables and benches and lots of big trees for shade or hiding behind to play hide and seek