Internet is definitely the way to go. You can use their terminals for .50 a minute or you can get unlimited usage in the room for around $100-120 if I recall.
Cell phone is a good option from many islands (I was able to use my cell from San Juan with no additional fees) but service from island to island differs based on what carrier you use. Some islands offer 3rd party service that prompt you when you dial out but I found it difficult to get rate info. Prepay phone card bought prior to sailing is probably best bet.