For paid campgrounds, I like General Hitchcock campground the best. It's shady, next to a stream (or dry streambed depending on time of year), has lots of trees and cool rocks to look at/boulder on.
For free camping, there is primitive car camping off Mount Bigelow road and a few spots off Incinerator Ridge road. If the gate is open for the road up above the ski area, there are some walk-in primitive spots in a patch of trees on the inside of a gentle hairpin turn, just across the street from a dirt parking lot with a bunch of ski lift equipment (would be a good basecamp if you are doing a bunch of days in a row at the summit crags)
Also, if you do stay at a paid campground, foraging for firewood is not easy; the areas are pretty picked over. But if you drive 2 minutes away from the campgrounds there is plentiful wood to be found you can load in your car.
I had offered to pay someone's camp fees for the weekend if you would share the spot with us. We are a family of 3 with a pop-up camper and probably won't be around camp much as we have family down in the city. I'd like to get a spot at Gordon/Hiribashi (spelling?) the weekend of the 20th. We will roll in at 8ish. If you could get the spot for us by Friday the 19th. I'll reimburse you or bring a sixer and pay the rest of the weekend nights. I can probably afford (it's 10 bucks per night) to pay your Thursday night too if you show up on the 18th Thanks! Steve