Silver River state Park is a very nice park. It has a long path through the woods to a kayak launch. You can also drive to a county park directly on the River on SR 40 and launch any size boat there on regular boat ramps. It's a fun trip. Take bread so you can tie up at one if the "Don't Feed the Monkies" signs and feed the Monkies.
You can have fires when there is no ban in dry season. True no swimming area. It's a strong run and kids would drown. Plus destroy the delicate vegetation.
You can have dogs. Take ours all the time. True no dogs on the trails. Too many bears.