I haven’t had one of theirs in a while, but Chick-fil-A might be the winner. Sonics is okay, I prefer their variety and times when it’s half off. Checkers has a decent banana shake. Speaking of banana shakes, the worst shake I ever had was a banana pudding milkshake at Krystal. No idea if they still make it but I actually felt physically sick after consuming it. It was either too rich with sweetness or super disgusting. I wish I could remember but I’d rather not lol.
Cookout shakes are indeed the best, though sometimes they're a little too thick.
My hometown has a place called G. D. Ritzy's that has the best shakes. It used to be a national chain but basically ended its franchising and now there are only a few in the US (mostly southern Indiana and a couple in Texas).