Abolt338, There are a ton of places to camp in the Winthrop area. It just depends on what type of camping you want to do? RV? Tent?
Pearygin State Park and the new side (old Derry's) always has slots open (during modern rifle) if you have to be by a shower, and they do allow fires in their pits as well. Up the East Chewuch River there are hundreds of camp spots along the river. Bear Creak Campground (both East and West) and the cougar flats area are usually pretty full with the same people coming back every year. There are quite a few spots up past Mazama towards Yellow Jacket creek and Harts pass as well. We use to camp on the FS Rd between Bear Creek and Pearygin Creek until they closed the road after the fire in 2004.
If you are going up for the modern rifle, I would suggest you take a drive up and look around then make a list of the spots you like. We usually Leave our house in Puyallup around 4:00 am on Friday before the opener and three years in a row we got our same spot. I have never "not" found a decent spot to camp. In the 20 + years we have been going up there I believe only three (that I can think of) had the fire ban on during modern rifle.
It really does not matter where you camp if you have a vehicle, there are many areas to hunt.
We have camped at East Bear Creek since the 2004 fire, but we may hunt Volsted one day and drive up towards Cub Creek another or down to Twisp or up Loop Loop for grouse.
Unless you "have to" hunt right out of camp it really does not matter where you camp.
Disclaimer ! I just realized you were bear hunting, my perspective was from the mid October (modern rifle) sorry if I cause confusion.