I visited this port twice. It is a tendering port, a new stop for cruise ships and does not have much to offer that was close and easily accessible to the main dock. The main city area has a very limited shopping area, a few duty free shops but not much. The
The second time I visited this port I responded to a Cruisecritic roll call and was one of 33 people that booked a day at Playa Rincon (which is supposed to be one of the 10 best beaches in the world). Getting to Playa Rincon is a challenge, there are two ways to get to Playa Rincon by boat or by car. You can google "Playa Rincon" and get tons of info as it is a very nice beach.
By Car; I was told it was a lot shorter but a very rough road and will take about 1hr.
The entire group 33 of us booked this with "Casa Dorado" they where very professional, I have a link to their website further below(see Samana) but the website does not tell the entire story. At Playa Rincon beach which is very lovely you can rent chair and shade for ($5.00/per chair) so be aware. On the beach there where a number of small places to eat and a place for a massage and renting Kayaks. Do not waste your money and pay for a snorkel excursion trip, you can snorkel for free right on the beach in the rocky area. Overall, I would make Playa Rincon my stop and not waste money on snorkelling or shopping. Very time limited due to the amount of people a lot of time was wasted waiting around but it was a nice day, suggest a group of no more than 10-11 and go direct to the beach at Playa Rincon.