I flew directly into Santo Domingo the day of the cruise and went directly to the ship. I used Royal Caribbean transfers to the airport which I highly recommend. I easily found the agent when I got off the plane and he stayed with us while we got our luggage and got us through customs very easily and quickly. The scene departing the airport was rather chaotic and I was glad I had someone to guide me to my transportation. Everything was handled quickly and efficiently - no long waits. I am a person who usually makes my own arrangements to and from an airport but I was unfamiliar with this port and from talking to others who took a cab I think it is better to just use the RC transfers here based on ease of getting through the airport and also the cost is generally less than a cab.
Getting on the ship was easy. There was no line when I arrived (about 2:30PM). There were lots of agents standing at the counter but they were all talking to each other and I had to wait for a couple of minutes before one would talk to me which was a little irritating. There was a short line to get your picture taken before boarding the ship but no longer than five minutes.
My cabin was ready when I got on board. I ended up just picking up my luggage in the hallway as I saw it and my cabin was not far away. No one seemed to mind and that way I did not have to wait as long to get it.