There is good reason why the Big Darby River is one of Ohio's only National Scenic Rivers, because it's beautiful. You can't have a bad trip on this river. There is wildlife at every bend in the river. I've seen every beautiful bird there is in Ohio on this river and the natural scenery is enough to want to be in the river. The river can be very fast and fun in the spring and makes for a great leisurely cruise in the summer. If you like to kayak or canoe, you have to do the Big Darby
There are a few dams you will need to portage, but you can see them ahead of time. Also, the book points out the exact location of each dam.
No fees or permits required. Just make sure your boat is registered, but you knew that.
This is what maps are for. Just locate Batelle-Darby Metro Park and there is the river.
There are places to launch all along the river. Most of the bridges you are allowed to park at and the park has a really nice launch area.
I used the book, "Canoeing and Kayaking Ohio's streams and rivers." It is excellent with descriptions and maps.