I lived in Kentucky for 4 years. Now reside in Cincinnati. In western Ky. the area around and in the Land Between the Lakes is your best bet. Columbus Belmont state park is nice, Paducah has a decent part of town along the river, and going out to the the Kentucky State Reformatory in Eddyville is an interesting ride.
In the south most people prefer the area from Lake Cumberland and Dale Hollow Lake east toward Pine Mountain and Middlesboro. The area just south fo there near Norris Lake is also really nice.
The area around Lexington is Bluegrass Country, lots of pretty horse farm roads.
North of there is, as one poster already noted, some truly outstanding roads that not many poeple know about. Routes 10, 22, 26, and 32 are wonderful.
My preference is to get a cabin at Pine Mountin State Resort Park and ride south from there. As pretty as the smokies, but much much less crowded.
Southern West Virginia has some fantastic roads that are nicely paved and well marked. We did a couple 3 day trips there in the past month using Beckley as our home base. Our favorite 'Sporting' route is highway 19 South as it zig-zags near Interstate 77 then Westbound on route 10 just west of Mataoka where you'll find a short section of road that rivals anything the Dragon has to offer.
Down by Pike county and Williamson, West Virginia, is the start of some fabulous roads. 119 to lexington is a pretty drive and south from Williamson on 49 is nice. There are lots of old appalachian roads and hollers to explore. But, don't stop in Matewan.... just a heads up.
I've ridden all over eastern part of KY on everything from Harley's, BMW's and Honda's. My current ride is a Honda 919.
Last year we picked up a new Harley for my buddy in Pikeville (richest county in KY and one of the richest in the eastern part of the US, not bad for a bunch of illiterates). To break his bike in, I chose a ride that took us up in the hill country and down around Harlan. This is an incredible ride. I left my house at 6:00 AM and I got home at 11:40 that night. We ride long, long days. No crying allowed. Anyway below is our trip and I actually started it from West Virginia for your convenience.
Begin at Williamson, WV which appears to be on the border of West Virginia. Take Hwy 119 to Hwy 23. Head East (left) on Hwy 23 until you get to Hwy 119/23. This is one of the most beautiful rides I have ever been on. People were very friendly when we stopped for fuel and sodas. You will see majestic mountains and valleys that only God could have dreamed up. You will go where eagles soar and bear roam. The switchbacks on Hwy 119 are also incredible. Bring extra cash as some of the gas stations my not accept plastic. Stay on Hwy 119 until you reach Hwy 25. Head west on Hwy 25 until your reach Corbin. Head north on Hwy 25 until you reach Lexington, KY. This is a mid sized town and a good turning point for your adventure. Once in Lexington find I-64 and head east until you come to Bert Combs Mountain Pkwy. Once you get to Bert Combs Mountain Pkwy head east. Make sure you stop at Natural Bridge State Park and climb to the top. Also ride through the Red River Gorge which is located just 5 miles from Natural Bridge. Head east on Bert Combs Mountain Pkwy until you reach Hwy 460. Take Hwy 460 to Hwy 23 south. This will take you back to Pikeville.
I guarantee you some of the most breath taking scenic beauty in Kentucky. There are state parks along the way so plan your trip accordingly. For me this is a one day ride but for most it would be a perfect 2 3 day trip.
According to my sometimes trusty map software the trip would be 500+ miles.
I apologize for any grammatical errors or misspellings as I am from Kentucky and we are the most illiterate state in the US (at least to some).