Avoid internet on the ship if at all possible. The cheapest you can get is a 240 minute package. SOunds like a lot, but at ship speed, it isn't.
Eastern....St. Thomas, if you walk toward the chair lifts, just before the building where you would buy the tickets there is an Asian restaurant. Internet is $3 for all day with a good connection, cheaper if you buy a meal. You'll see plenty of CMs hanging out there. There is also an internet cafe in Havensight mall, but it was also a bar and we honestly didn't feel safe there. The restaurant was very crowded and totally felt OK. There used to be an internet place right at the end of the dock--it has been converted to a Senor Frog's.
The above was accurate as of December 2011.
Google "cheap internet name of port" to have some good ideas in advance. Then talk to the servers/stateroom hosts. THey know where the good places are.
We haven't done internet in St. Maarten for a couple of years, so don't know if my info there is current.
If he MUST use it on the ship, go on, download what he needs and log off. Do the work off line, then log on and hit "send." Alternatively, if possible, save the work and send from an island.