First place that popped in my mind was Fountain City duck pond, but that's N Knoxville. And although I haven't been there in decades, I have read that it closes at dark because of the homeless people....but no first hand knowledge.
Also thought of Buffalo Springs WMA....but it's under delayed harvest regs right now.... artificial bait only...and catch and release.
Lastly.... If you're just looking to catch a fish and aren't picky about size or species...I would go to the boat ramp at Cherokee dam (on the lake side). Super easy access...drive right to the water. Not suppose to fish from the floating dock, but nothing says you can't stand to the side and cast to it. People do it all the time. You can also walk back in that cove... towards the primitive campsites. Surely through there somewhere you can catch a bluegill.
A little farther away...there is Grainger county Park...and boat ramp. Can fish anywhere around there. Across the cove is Greenlee campground and access area. Should be able to fish the cove from that side.
Wife just informed me there is a bass tournament launching from the dam ramp tomorrow....might want to skip that...up to you. Unless of course he likes looking at boats..
That's all I can think of right now...from the bank.
Good luck