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We were on the Norwegian Gem in June, the name of the terminal will be on the travel documentation you receive - if your mum shows this to the taxi driver there should be no problem. There were only 2 cruise liners in port when we took our trip. I think I did see the option to pay in cash - but believe that you have to pay a certain amount upfront when you check in. Check on NCL website - they have a phone number on the top right hand corner you could ring and ask, althouth, I rang them a couple of times on different issues and some of the people I spoke were more helpful than others. I can't comment on trips provided by NCL as we nearly always do our own trips. I have found that most citys have Hop on Hop off buses and the smaller ports of call usually have 'tourist trains' that are good. Have a look at our review under NCL - all ships (messed up name of ship) and that might answere some other questions you or your mum might have. Hope mum has a great time.
The terminal is about 5 minutes away by taxi.