Since I found them all ;-) in all three locations here ya go.
Cozumel: (this is the trickiest one to find) It's just off the Main Town Square in Cozumel, on the Hotel side (farthest away from the International pier, it's in a little strip type mall on the second floor). I do recall seeing one right near the pier, but the closer you are to the ship the more expensive things tend to get.
Grand Cayman: As you leave the Tender dock turn left head along the shore. Cafe is on other side of the Road (2nd Floor again), about a half a mile from the Tendewr Dock.
Jamaica: (Easiest one to find) It's in a little building on the left side of the Cruise Ship compound. I think it was the most expensive of the three, but it was the closest to the ship as well.
Average cost is about $3. for 15 minutes. Victory's Internet Cafe was 75 cents a Minute in comparison.