Like the previous reviewer, we camped off the Huckleberry Trail. We parked at the summit, descended down and came back up. It was one of the most gorgeous trails I've ever experienced and highly, highly recommend it for a quick weekend backpack.
We did this hike in March and there was a thin layer of snow on the ground when we started that quickly accumulated while we hiked and then overnight as we slept. Quick heads up to be prepared if you're going to do this because I definitely got pretty cold and chickened out without doing the whole trail.
This was the guide we were going to follow: https://www.hikingupward.com/MNF/SpruceKnobSenecaCreek/
The sites along the beginning of the trail are nestled among the spruces and very beautiful if you can't make it too far on your first night. We camped just before mile 5 where you get on the Lumberjack Trail, there are two nice sites there with defined campfires.
These are all backcountry, hike-in sites, so none of your campground amenities, but they're all gorgeous.
Spruce Knob Lake is an established campground at the base of the mountain. It was closed in March when we visited so we couldn't even drive through. If you're going to camp at this campground I would totally recommend doing the Huckleberry Trail at the summit!