Thread necro on my part, but IMHO the cheapest indoor tennis club rate is to be found at the Queens College Tennis Center:
Queens (N.Y.) College
The non-member rates are already quite good, but the member rates are what really make it a bargain.
Keep in mind that there is no pro shop there, so neither tennis balls nor rackets are sold.
Also, bathroom access is limited (you have to use the college restrooms) and not connected to the tennis center.
With those caveats in mind, the Queens College Tennis Center has the cheapest hourly indoor rates in all of NYC.
As for Manhattan (what most non New Yorkers think of as NYC proper), the cheapest rates tend to start around the $75/hr mark for indoor tennis (very early in the morning or very late at night).