This spot is only 30 minutes from downtown Asheville. Plan a day hanging out downtown, then hike the Craggy Pinnacle Trail and see a 360 degree mountain view.
I usually spend the day visiting restaurants and breweries around Asheville. Before it gets late, so you can enjoy the views, head to the Blue Ridge Parkway located right outside the city. After about 30 minutes on the parkway, you will park at the Craggy Pinnacle parking lot Milepost 364.1.
From here, there is a short and beautiful half mile hike to the peak. Once you get to the top, if you take a left, you'll see an overlook with 360 degree views. If you continue to your right, there are grassy nooks.
If you feel like camping, the closest places are in the Pisgah National Forest, and you can find more here.