Shasta will be hot - no breeze to cool off at night. But the water level is at about 95 percent.
Lassen might be better.
You could try the Lakes Basin area in Plumas and Tahoe NFS. There are a bunch of campgrounds - some non-reservable. Lots of lakes. Little towns along Hwy 49 (be sure to get shakes at Bassett Station).
August is going to be crowded no matter where you go, so don't make that a "no go" reason. Just know there will be crowds and accept it for what it is. I'd rather go with the crowds, than cancel and have life prevent another opportunity.