I'm guessing if you have a Planet Fitness membership to a local branch, your best bet would be to see if you can upgrade just for one month to the plan that gives you access to a branch in NYC, then downgrade back after.
Planet Fitness, Blink, and New York Sports Club I think are the big budget gyms in NYC, and I'm guessing any type of a 1-week membership or 1-week trial is something you'd have to haggle for and contingent on who happen to be talking to when you inquire.