"Till" should be accepted as an alternative, or "pay desk". This is after all a question that would only be asked in a department store - in a supermarket you can't get out without going through the checkout, even if you haven't brought anything.
That sounds a bit odd. In a supermarket it is usually the 'checkout' or 'the tills', but in a shop I think I usually ask where the 'till' is, although that is the machine with the cash in it on the cashier's desk, not the desk itself.
Probably quite a few variants!
Yes, in a shop or supermarket, 'checkout' is usual, but I was having a Senior Moment and was thinkng of a Post office or a bank, where 'cash desk' or 'Pay desk' is usual.