St. Peter's College sells memberships to its athletic facilities (including indoor tennis courts). If you aren't an alum, space is very limited (and I've never tried to join so have no idea what the waiting list looks like) but it might be worth a call to see and/or trying to find a partner who's a member and can get you in. http://www.spc.edu/pages/1609.asp

There's also Midtown Tennis Club in Manhattan and the USTA courts in Queens (which would be super convenient if the #7 extension ever happens).

And you might hit up the Hoboken Tennis Meetup with this question - they're likely to have more insight. http://www.meetup.com/hoboken-tennis/

I've used the Binghamton Club up in Edgewater (a longish drive though).

Does anyone have any recommendations for indoor tennis and racquetball facilities in Jersey City or the surrounding communities?