We stayed there last year. Beautiful park.
From Rt 460/80 until you enter the park is a 2 lane road with a lot of curves. and a good size hill near the park (probably about 25 miles worth of small roads)
It's is doable, just make sure you fill up with gas while you are on 23. Not a lot of gas stations after that point. Take your time, there are still coal trucks on that road.
In the future maybe 6 more years there is a new road they are building from Pikeville, KY to the Breaks. The road is done, but the bridges are still being built.
pictures at the park