On to the first port of call, St.Maarten.. I had been there before so I was only off the ship to pick up a few things at the local port shops.. the beaches in St.Maarten are second to none and only Turks and Caicos, in my opinion, beat the ones that you will find (on the Dutch side) of the island so if you are looking for the best beach be sure to check them out here. The one complaint I heard from those that took the beach excursion was that they went to the French beaches which have the rough water so unless you like wind surfing you may want to stay on the Dutch side.
The second port was St.Thomas and I had also been here.. not near as nice as St.Maarten with regards to the beaches but still pretty nice. Many opted to take a cab over to the water taxi where you can then go to St.John island and take in the very nice beach over there. I did that the time before and quite enjoyed it but depending on the amount of time you have, which is not as much on Epic as it was on my Carnival stop, so I think I would advise staying in St.Thomas for the day. The shopping in the port here is very good so you actually don't have to go far.
The last port which I had never been to, Nassau, was what I would consider not just a port shopping as you were right in the heart of the downtown area or so it seemed. Full of activities restaurants, coffee shops, etc, easy to spend the afternoon and in our case, again, not that long since we arrived at 11am and were gone by 6. Most definitely not worth the trip to Paradise Island for only half day but if you are going to go check it out, you can get a cheap water taxi for $8 round trip right as you walk in to the port entrance.