We had dinner with my mother at Top 'O The Lake in Guntersville on Saturday afternoon, and when we finished we still had several hours of daylight left so I pulled up Google Maps on my phone and searched for "waterfall". It brought up several that were nearby and I picked Thompson Falls on Mink Creek and we headed that way. It was about a 15 minute drive and the "road" to turn off to get to the falls is only marked with a No Dumping sign.
If you go here, take a vehicle with high clearance and you shouldn't have any trouble driving right up to the old bridge that is just above the falls. The road is bumpy but is mostly rock so there shouldn't be any issue with getting stuck.
We weren't ready to do any real hiking since I had my new sneakers on and Jack only had flip-flops, but there is a trail that leads down to the lower two cataracts.