The area around Lexington is very nice. I do the Horsey Hundred every Memorial Day weekend out of Georgetown Kentucky and really enjoy it.
That said, I'm partial to eastern and middle Tennessee for riding. I've done the Bicycle Ride Across Tennessee a couple of times now. It's a weeklong tour that generally goes from state park to state park. The name itself is misleading in that it doesn't go across the state. Rather, they pick an area and do a big loop. The roads in Tennessee are great and most have a significant shoulder. They offer lots of pretty scenery. There are several books on cycling in Tennessee with maps and suggested routes. I did a ride two years ago near Franklin, Tennessee (south of Nashville) and really want to go back to that area in particular.
I tend only to use the roads in state parks as "thru" roads. For the most part, they don't typcially have much of a shoulder and there's a fair amount of traffic on them. I wouldn't center a ride around them. I have only been to a couple national parks. Those that I have been on were rideable, but there was a lot of traffic.
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher