We were on the Grandeur in Sept. There is an internet cafe. It's right in the open on one of the upper decks (6 or 7 I think). It's never closed. There are only about 10 terminals though. I used it to send my kids email & to receive news from them. It's very slow and it cost me about $5.00 everytime I was on it. There is a printer available, so when I received emails I wanted to read I just printed them instead of reading them at the terminal. It didn't cost anything to print them, but you're paying by the minute to read them!
Hope this helps,
Have a great time on the Grandeur, we loved it!