There are these Yolas that head for Puerto Rico cada rato.
Some cruises out of La Romana do not require Visas for Dominicans for the port stops they make. The cruise line has some sort of deal taking responsibility. At least in the past they did it. Do not know about now, but check with a good Travel Agent in SD. But no Passport forget getting on board.
If you have a Uk passport there is not much problem - La Romana to the Windward Island -
BVI , Antigua, Dominica ,Martineque and St Lucia is quite a good trip. Worth doing too as you can compare the different Islands.
There are also a lot of RE-Location cruises going on to Europe at the end of April /May - these are good value.
Try Voyages to Go - dont have the website at present !
Olly and the Team