You shouldn't have any difficulty getting a walk in at Tuolumne Meadows, they reserve half the sites for FC/FS. On a Thursday, even less of a problem. Office opens at 8:30, just be there around that time. Ask for B45, B46, B47 or B48, those are on a back loop and you won't have as many neighbors.
If I am wrong (it's happened

) there are campgrounds just outside Tioga gate at Tioga Lake and Ellery Lake. But I thought we would have to go there, as we got to TM around 9 am, only to find there were plenty of sites at TM left. They sold out by 10:30 - 11.