This started just last year.
NYC Parks put some moorings in on the Manhattan side at Pier 40 (Houston St.) by Holland tunnel air shaft. I believe the overnight mooring price was the same as 79th St. if you could find anyone to pay the fee to. No launch boat at Pier 40 so you need a dink same as 79th St.
They added more moorings about 1/4 mile to the south, just above the what is called the World Financial Center. These moorings are now operated by Liberty Landing which is almost directly across the Hudson. I believe they are charging $75/night for transients. There is a launch there (of sorts) and it is fairly convenient to the subway.
Both of these mooring fields are nestled between piers that stick out into the Hudson so there is some protection from the prevailing currents unlike 79th St. There is still plenty of ferry traffic though so it could be a bit bouncy at times.
Both of these mooring areas are a few blocks from my apartment here in Tribeca which is how I know about them.