my response might be too late but i guess for a future visit there’s Yoga to the People at 38th street and 6th avenue: http://yogatothepeople.com/new-york/38th-street/
I personally go to the Hot Vinyasa class. They have a traditional hot yoga as well.. Each class has a $5-7 fee per class, $2 mat rental, $2 towel rental and $1 for a bottled water. I would recommend coming to class about 20-30mins before class to be guaranteed a spot. It’s first come first serve.
You can’t beat the price! The instructors there are pretty awesome too 🙂