It'd be a bit of a drive for you, but closer than Minnesota, but the Meramec River is pretty nice to float down (over by Meramec Caverns in Sullivan, MO). I did that once or twice and it was enjoyable.
meramecpark.com/floating.html

they make things to keep the cooler afloat, I suggest doing that because if not water tends to get in and your cooler sinks.

we put it in a tube and tie it to us

We rented tubes. It was our first time down the Cannon. The drive there from the Cities sure is nice. I've never appreciated how beautiful a corn field could be.

I love tubing like this. Having water wars on the river is always fun.

We wanted to go to war with some of the crazy college kids, but considering that the average person in those groups was twice my size, I thought it'd be best to let them be.