Captain William Clark Regional Park at Cottonwood Beach
A great place for either a dike top paved walk or a beach walk, or both.
From the parking along Index Street, you could walk west to Steamboat Landing Park, or east to Steigerwald Lake Wildlife Refuge. Note that while you can ride your bike or walk your dog on the dike trail, you cannot take either into the Wildlife Refuge.
When I was there this summer, there was a sign warning of a cougar siting in the area, but that sign has since been removed. Cougars roam a large area, so it is not surprising that one might be seen in an area and later not be found there.