Look at hotel prices in Manhattan, and they regularly hit $250 or more for a total shithole like a Holiday Inn Express or a Hampton Inn.
So a provider basically gives half a session for free just to pay the hotel room, IF she can find a $250 rate.
The other thing that kills your equation is the cost of just eating out here in NYC. Unless you plan to eat pizza slices all the time, your budget better be close to $50/day just for nothing special. If you want to have a few respectable meals like at, say, Hillstone, then you can easily start looking at $100/day for food.
If you live in other cities, it ain't nearly as bad. Chicago is about 30% less, for example.