Ponderosa State Park is the go-to campground near McCall, but it's likely to be fairly crowded on weekends and holidays. Others might have recommendations for camping areas a little more off the beaten path.
You can dispersed camp practically anywhere in the area. There's a huge amount of open forest service land there that's almost all fair game. Drive a few miles up Lick Creek, Warren Wagon, Old Brundage Mtn Rd, or pretty much any road through Forest Service land and you'll find something. Where are you going climbing?