Yes they still exist, they are now known as radio taxis. These taxi cabs tend to be comfortable with AC, they don't stop around like Publicos, and many of the drivers have some very interesting stories to tell. They will even cross the entire country if you ask them to, well you being Dominican you should probably know how nice Dominicans are!
Anyways, if you are driving from Downtown La Vega, make sure you get on Highway 132 or as it's much more commonly known, the La Vega-San Francisco de Macoris Highway. Once in San Francisco de Macoris (notice the nice mansions there, impressive) make sure you get on the San Francisco de Macoris-Nagua Highway. Technically it's still highway 132, but nobody know the roads by their number in the DR. Once in steamy but pleasant Nagua, make sure you get on Highway 5 or the Nagua-Sanchez Highway also known as Carretera Luperon and that Highway will take you straight into the idillic Samana Peninsula. The Highway passes right through the town of Samana and finishes at Las Galeras. If you are headed towards Las Terrenas or Limon, turn at the turnoff on your left onto a spankin newly paved road after the town of Sanchez. The road ends in Las Terrenas, enjoy the magnificient views!! Remember, if you get lost, just lower your windows and ask for directions from a Dominican that seems in a good mood to ensure a kind response, especially if it's a very hot day. In general people are nice, but it's not nice to bother people when its hot and humid and its noon! Well, you know! Enjoy your trip!!