From what I experienced, there seemed to be two kinds of taxis. The first are the established system of taxis that work off a centralized system and charge higher rates. They are mainly targeted towards tourists. In smaller towns they tend to congregate at taxis stands/stations. In town transport is somewhat reasonable, but travel in-between towns and they will gouge you with a tourist rate. For example, a trip to Puerto Plata from Sosua will cost $22-$25 US. The same direct trip on an air-conditioned Caribe Tours bus costs less than $2. Check the Caribe Tours topic for travel between towns and cities.
The second type of taxis are some kind of private or taxi service targeted for locals. I only found one such place in Sosua on the advice of Fantasy. The location is Green 7 on my Sosua Map. I used this service once when traveling to Puerto Plata from Sosua. The cost was 300 pesos, just over $8 US. I don't know if similar taxi service is available elsewhere, but I have doubt that the locals are paying the same high rates.
Here are pics of the Sosua local taxi terminal
I highly recommend using Caribe Tours when possible. If you are in Sosua and need a ride to the airport, I would recommend coordinating this in advance to get a reasonable rate from one of the less expensive taxis.