Do you pay to Touch-and-Go?
It varies.  Some airports charge by landing, others by operation (a series of landings if training).  Some charge through the FBO, who may waive the fee with fuel purchase.  Expect that multiple landings at BOS or JFK will result in multiple fees, often billed to the registered owner.  It was a while ago, but I did a series (about 12) of landings at BOS one night, and the owner/operator paid 25 dollars each. Someone told me recently that the fee was more like $65 now for a Cessna P210.

To be clear, call the airport and ask them, or check their web page, which may have their charges and rules on it.  And/or check with an FBO or two at the field.