I got a personal email thru this board and I am not sure my response went out correctly, so I am posting it here--
The Elk can be very hit or miss, especially this time of the year. The good news is that because of the drought, you will not likely have any generation to interrupt your trip or day. I have been there three times in the last two weeks and have only caught four fish. (My luck changed on Saturday. See separate post on this.)
The Elk is a stocked river and of course fishes best when it has just been stocked. You can probably find that out from the TDNR website.
Unless you plan to float it, there are only two public access points for the Elk, another consideration. One is right below TF Dam outside of Winchester and the other is on the Moore / Franklin County line at Farris Creek Bridge. I believe based on my recent experience, the best fishing right now is below the TF Dam stretch. Start at the bridge and work your way down to the Big Bend which will give you about 1/2 mile of good, easy wading.
I fish it because it is close to me, easy to wade, generally light pressure except for the weekends. If you go, stop in Lynchburg at the Fly Shop (Tim's Flies and Lies) right off the square. That way you will get the flies you need. I believe they are closed on Wednesday. Check their website and call ahead before going there is my advice.
Hope this helps,
RobertS618