If I recall correctly, there is a flat rate from MVD to downtown. Somewhere in the neighborhood of $20. Perhaps a bit less, but it didn't seem to be any bargain to me. There is also bus service from the airport to Tres Cruses, the bus terminal in the city.

Regarding the new terminal, it was supposed to open in mid-November. When I stopped by the Pluna office in Punta del Este last week I was told it was open, but simply not in use. Go figure! Now I am told it will be in use by mid-December. I hope to make use of it on January 3rd! I would bet it is a beautiful facility.