Ula's Day Spa is a small spa located in Tribeca (feels like the middle of nowhere) near Nobu, Chanterelle and several other wonderful restaurants. It's tucked away on a side street and once you enter the spa, you're greeted warmly. There are spa products to purchase if you'd like and you walk through the nail area to get to the spa. The actual spa rooms are on the main level but the locker room, suana and tea & fruit area are all located downstairs.
I really recommend showing up early to take advantage of the lovely snacks and to simply relax. When you're ready, head back upstairs for a lovely, low-key, no sales pressure massage. Have had one of the best massages of my life there and was saddened to hear that my favorite massuese no longer works there.
Still, it's a very personalized experience; I like it better than the large spa institutions.