Wish I could be the guy to help you with this one. I know both the Elk and Tims Ford are great Smallmouth and Normandy is well known for Bass & Crappie. All are within a 45 minute drive from home and I have never been on them. Another that flows through the area is the Duck and is a super Smallie river. I never wet a fly until last weekend (except about 30 years ago and that doesnt count). The folks I have talked with on occasion about Tims say its best at night .
Sorry but I havent fished those waters at all.No real reason other than I usually fish the Caney Fork or Stones River which is the Center Hill (Smithville Tn. area and its not all that far from where your targeting)
I would suggest concentrating below the Normandy dam and Tims Ford TVA: Reservoir Information
Be sure to check the link for release schedules. THE ALARMS ARE NOT DEPENDABLE AND WHEN THEY RELEASE YOU BEST RECOGNIZE ITS HAPPENING AND GET OUT OF THE WATER.
Also buy a copy of the Tennessee Atlas & Gazetteer at Barnes and Noble when you get the chance as it will show you the accesses and landings etc. I use it to pick my steams and ways to get on them.
If you go below the dams on a weekend there will be plenty of people in the water and will put you on the right fly. A lot of the Rainbows here are caught with the artificial salmon eggs pink and chartruse.
I mentioned that I just caught my first fish on a fly rod this last weekend and boy what a thrill but I fish mostly for Smallie and had always used a spinning rod. Well that is changing.
Also when you get a hotel picked out Im sure they can point you to some good tackle shops in the area. If you get a chance the BPS in Nashville on Briley Parkway has a great fly shop (really worth seeing and leave your check book at home
Google Manchester use the satellite and zoom the dam (Duck),TimsFord (Elk) and Hurricane Creek above Tims is suppose to give up some good Smallie.
My fly fly of choice is a little brown one with a yellow thing underneath
Im at the same part of the learning curve with a flyrod as you are. If your spinning I say black rubber worms they NEVER fail.
If you go below the Dams you'll have plenty of company on the weekends.