They set up their own sites. The nearest one to us was in a abandoned JC Penney. (15 miles but then we're 10 miles away from anything anyway ;-) Plenty of space for boots and fainting area. The appointment website was a snap. CVS, OTOH, was a complete disaster. You had to pick a slot first, then fill in endless screens of personal and insurance info. By the end, the slot was no longer available. Start over. And no, it did not remember any of the previously entered data. (But I guess improvements have been made?)

By the time the boosters came around, the site had moved to a smaller spot and was operated by walk-in as well as by appointment. I walked in and got the shot within 15'.