In the States, they tow your car to a yard and hold it ransom until you fork out a $1K or so (depends on the state/municipality), with accrued daily surcharges. And, good luck finding the yard. They also only take cash or debit so that you cannot run a chargeback later on. I'd rather just pay a $300 ticket, don't tow my car.

Can you sue them for not telling you where your car is and then to recover all fees resulting from you not knowing where your car is?

I suspect you could but you'd be risking a car - better try it with the clunkiest clunker you can find.

You can try, but you won't be the first and they are going to have lawyers for this exact scenario with decades of legal rulings and legislation often in their favor already. It's not usually worth the time unless you are willing to risk losing many thousands in lawyer costs if you don't win.