For a
very inexpensive option, NYC's Dept. of Parks and Recreation runs several fitness centers in all boroughs. Some have pools, and pretty much all of them have spaces for strength training, cardio, basketball, etc. Be forewarned - they are not very high-end at all. But they're clean. Floor mats? I assume so. It's been a few years since I've been to one. You would have to check out the facilities near you or convenient to most of your friends.
The membership is $50/year for access to the centers without pools only, and $75/year if you want to use the pools. I believe that when you join, you have access to all of the facilities (of the type you pay for) to work out on your own, but classes are extra. Also, not sure if this is for a limited time or not, but the website states that
all the centers are free on Mondays to non-members, as part of something called "BeFitNYC Free First Mondays". Here's the link:
Recreation Centers : New York City Department of Parks & Recreation. Click on the tab for your borough to find the center nearest you.