Yes, its true, you'll find the internet cafe's pretty close to the pier, a lot of the ships crew like to use them as well. If you have a hotmail or aol account, its easy to access your e-mail and you can usually use an hours worth of time for around $5.00, much cheaper than the ship and usually a DSL or fast connection.
In St Thomas, Cyberzone, is probably the closest internet cafe. They're ACROSS the street from the Havensight dock in Al Cohen's Mall. You can also rent phones and buy phone cards there. Beans, Bytes, and Websites is another internet cafe in town.
In St Maarten, there's an Internet Cafe UPSTAIRS, but unfortunately I can't remember the name of it, or exactly where it is, but it's on the main street, close to the dock.