Depending on time and season. Just know that The Parkway is Federal so speeding can have different consequences. A Ranger humbled my partner when he ask him if he knew where the hell he was and what it meant. The Ranger told my Buddy, " I am supposed to take your ass to jail in Virginia till you see the Judge on Monday, but Monday is a Holiday, unless of course you have $2200.00 cash bond in your wallet. Do you have $2200.00 on you? Then I suggest you slow the hell down. " We were doing 10 over when he pulled my partner. He pointed and screamed at me to keep going when I started to pull over and stop with them. Figured he had a partner waiting for me but stopped and waited after about 5 minutes. That was in the late 80's but it left a lasting impression on me.
I am riding up to Pisgah 09/30 then heading for Suches the next day. Still want to ride the Pkwy to the Shenandoha Valley. Hitting Campgrounds then day riding.
I don't speed on the parkway so 250 miles would be a long day for me.