NY to SC trip suggestions?

I recently moved to Greenville, SC from NYC and am planning on riding my Honda Shadow Aero (750cc) down at the end of this month. I'm getting saddlebags and highway bars for the ride and leaving from Metuchen, NJ. Got my license last year and have a little under 3,000 miles on the bike, all of which I rode myself. I've got a National Park Pass which allows me free access to many NPS locations.

This will be my first road trip and I thought Reddit would be a good place to ask for suggestions and advice, so here I am. Any suggestions or advice?

I'm planning to take 3-4 days along route 81, but my mechanic told me that I should think about connecting to the Blue Ridge Parkway. I'm a little nervous about finding gas and places to stay, so I was hoping to find some experienced folks willing to give advice before I leave.

Will share photos of the trip afterwards for sure.

Thanks, Reddit!