Can you work out without a gym?
New York City has a lot of free fitness classes across the entire city.
Parks are often a great place to find free classes around you.
For example, Bryant Park in midtown Manhattan has free
New York city isn't the only place that has these and there's more than just these exercises. Meetup.com and other websites offer a great way for people to get together for all sorts of fitness activities which can be very cheap or even free in many cases. If you can't find something, you could try getting together with some friends and get something going that could really build up into something big!
Other than classes like this, jogging, power walking, and hitting the monkey bars at your local play ground are great ways to use your local environment. Doing push ups, sit ups, and even getting some weights can be a great way to build up muscles all without a gym. It can even be more motivating because you're switching up your environment and finding new ways to get yourself interested in working out.