You can cross the swinging bridge near Miss Lily's and fish on the other side. The property is Wellspring Resort owned by Jill and Steve (nice folks). They don't mind fishermen if they stay near the water and don't roam around. If the place gets trashed, they might change their mind.
You can enter the water at bridges. I wade around in town and nobody says anything to me. If you want to access the river at a business, ask for permission. Some home owners I know don't mind if you ask. I fish the lower end of town for smallmouth bass. Most of that is State Right-of-way.
Stocked trout move into the water near and above the last campground before entering the Park. That's a good place to fish.
That's a good start.