The ticket office, but not the cash register?
Kasse is a very common word. dict.cc has a long, long list of translations: http://www.dict.cc/?s=kasse Several of them seem valid here, cash register is one of them.
Thank you. I thought that was so, but it's hard to be sure that there isn't something in the context that alters things.
“cash register” is also acceptable.
cashier? it should be also accepted.
Cashier it the person actually operating the cash register.