I've done the entire BRP/Skyline combo several times - at a medium, slightly brisk pace with stops every 90 mins or so, slightly above the speed limit and hitting up the major tourist spots, it's a comfortable and amazing 3 day trip.
I've done the BRP northbound from Cherokee NC all the way to Front Royal in 2 very long days. It was midweek so there was very little traffic and the pace was quite brisk. You really need 3 days to enjoy the parkway. Also, remember that next weekend is Memorial Day in the US and the BRP is full of campers, hikers, cyclists, and sightseers (park rangers too) . I would avoid it on their long weekend.