In August 2019, my Mom wanted to go to the highest mountain within Virginia, so a quick Google check led me to Mount Rogers.
The drive was pretty long and roads are very rural once you get close, so keep that in mind when wanting food and gas. But the views were magnificant.

This was before Covid, so take a look at the State Park webpage before you head there to make sure that they are open. The Trail Guide can be found here.
Our main goal was the head up to the mount views, but there was tons of more things to see here. We did no camping at the time, but I imagine it is amazing as well. Spring 2021 we plan on doing actual camping/hiking there.
We went to the main attraction and after the Visitor’s Center, we hit Twin Pinnacles Trail.

The trip was only 2.8 miles, so not that bad, but obviously there are some areas that are very steep. We had to leave my Mom (in her 60s) before the climb up to the Big Pinnacle, so keep that in mind. It is a 21% grade to get to the Big Pinnacle over rocks.