Laurel River. I've not been there, but I have a couple buddies that do a fall trip in canoes there every year.
Cumberland River. FANTASTIC, but watch the water levels ffrom the TVA SITE.
In southern Indiana. Lots of trolling motor lakes. Hoosier Nat, John Hay, Deam, etc, etc.
I've also fished Jericho in LaGrange.......NOT bad there either.
Long Run Park in Louisville is not bad, but I have not been there in a while.
Also, also..........The Dix river. Paddle up from the KY. THAT is great fishing.
How about Lake Shelby in shelbyville. I've also been there, and it is good.
AND finally.........Floyds Fork......there are a couple good put ins along the river that are public.
I hope this helps........