On the last cruise we went on the interntet just long enough to check our email from back home. Our son was awaiting acceptance into his medical school program, and we were anxious to find out. Other than that, you won't find me near a computer either.
I thought I read somewhere that you can now also get WIFI, so that if you take your laptop, that might be a better alternative than that internet cafe. At least you wouldn't be stuck at the same place all the time. Every time we walked by, all the people there seemed to have that strange blue computer tan . . . and it was always the same people, night after night, after night. If I ever get that addicted to the web - when on a cruise ship, someone should put me out of my misery!