Big Bay Town Park is a superior park on Lake Superior! (See what I did there?) It is one of the parks on Madeline Island, the only Apostle Island that is not part of the Apostle Island National Shoreline.
There is not a playground, but there are trails and a great lagoon for swimming or kayaking/canoeing (available to rent). Lake Superior is really too cold for swimming, but this lagoon is nice and warm-ish...and gorgeous! We even saw a deer swim across the lagoon. There is also beach to play in on the shore of Lake Superior.