I adore Lewis Mountain. It's quieter than the other Shenandoah sites, it has clean facilities, showers, water, and a store, and is right on the Appalachian Trail with tons of access to other trails. The campsite manager is onsite if anyone needs anything, and is super friendly and knowledgeable about the area.
Overall, highly recommend.
I went to Blowing Springs as a last minute effort to get a site after the one I planned to stay at was closed. It was a nice enough site - not crowded, and on a trail.
If I recall correctly, it was cash only. The one trail that connects to the site is pretty and has water access, but was very overgrown when I visited. The area has a high population of ticks, so watch out in the warmer months.
Overall, decent, but not a site I feel the need to revisit.