LiveATC.net only offers the "mixed" feed (there is a limit to the amount of scanners and bandwidth volunteers can provide.) You'll sometimes hear tower 1, sometimes tower 2, more or less at random. If you want to listen to a specific frequency, taking your scanner to the JFK area might be the best solution.
(N.B. New York City has very good coverage on LiveATC.net; volunteers for other hubs are still welcome.)