For a little slice of Central Park in the heart of Cowtown, take the bridge over to this island, with grassy fields made for tossing Frisbees, plus bike paths and ample space to stretch out. During the summer months, you can catch a Shakespeare production in the park's natural grass amphitheater or check out the Folk Music Festival in July. You'll also find the upscale River Island restaurant here.
Watch yourself around the river. The water is cold and the current is strong and not suitable for swimming. The bridge to the island from downtown is at the north end of 3rd St SW, near the Eau Claire Market shopping area.