Even if you wanted to sail to the USVI you could still do it, in a roundabout way, without the required US Visa. This involves taking the ferry
from the BVI to the USVI and entering on the visa waiver (you do need to fill in the ESTA web document, though) and then with your I-94 form you could take the ferry
back to the BVI and then enter the USA on your sailboat.
Apart from the USA the Caribbean islands are open to Europeans without the need for visas. Several are part of the EU and French.
Coming up the island chain from Trinidad & Tobago
all of your passages will be in sight of land on the horizon, so with a 4-5knot top speed you will still be doing at most an overnight passage
all the way to the northeastern tip a St. Martin / Anguilla
. Then you have a big downwind passage
of 70nm to the BVI. But it is easy to spend one or two whole seasons between St. Martin and Grenada!