Mid-July in 2020, we had a most fabulous vacation centered around Sutton Bluff Recreational Area where we camped. Nearby at Centerville we visited the Black river underneath the highway underpasses. We have have spent the entire day wallowing in the river there. Then we visited Reeds Spring Mill in Centerville. We visited the Lower Taum Sauk Lake as we drove around exploring. In far-out-and-away-ville we visited Cooks Spring. Finally we visited a remote camping area not far away with a view. We also visited Lesterville Conservation Area and found it to be nothing exciting for us.
Cooks Spring can be found along the roadside, but I cannot locate that it is owned by any government entity, so it would appear to be on private property, but open to anyone up for a short exploration. To get to Cook Spring from Sutton Bluff, head out of the camping area back to the intersection of River Road and Highway 2236 and make a left onto Highway 2236 (aka River Road). Travel along 2236 and continue on the road when it turns into Karkagne Scenic Drive. Turn left onto Highway CC. Travel for 1.6 miles and the Spring will be on your right (County Road 848). It will feel like you are out in the middle of nowhere!
There is not much to see here, but it is a fun adventure. There is a concrete slab which I suppose you can set up a picnic blanket upon and listen to the water flowing. I understand there used to be a pavilion here. There is the remnant of the fireplace at the location.
Behind the fireplace and concrete slab is Cook's Creek.
This photo shows how close to the road and what type of narrow gravel and dirt road you will be traveling upon.
If you follow the sounds of water, you can locate the actual Cooks Spring. Here is a photo of it. The water spills out where you see a gap in this photo. It is a beautiful sound and I found it quite delightful. We followed the creek to where it crossed the road and the Spring is closer to where the creek crosses the road.