Ask Mr. Smarty Plants

The first place to go to find a list of potential plants is our Native Plant Database.  Use the Combination Search feature.  This will provide you with a big selection with a lot of choice to narrow down. Under Combination Search, select the following categories: State – New York, Habit – herb (for herbaceous), and Duration – perennial. You can narrow down this search further by indicating soil moisture, light requirements, blooming time and bloom color too.
These search criteria will give you over 1,000 perennials to consider.  Follow each plant link to our webpage for that plant to learn its growing conditions, bloom time, etc. At the bottom of each plant webpage, under Additional Resources, there is a link to the USDA webpage for that plant. Take a look there for more specific details about suitability before you put them on your final planting list.
You can also look at the Recommended Species for New York State. There are 112 suggestions on this list.
The volunteers and staff at the Wildflower Center who maintain the database have partners in different regions to help with these recommended species lists based on what is easy to access in local nurseries.

Your request for plants that have the longest growing season has me wondering. Do you mean longest blooming time instead of longest growing season? Except for the spring ephemerals which grow, bloom and then go dormant in the summer, most native perennials in New York do have a long growing season (April-October).
Note that our database will find plants native to New York State and not specifically to New York City. The City of New York Parks & Recreation has produced a publication on Gardening with New York City Native Plants that will give you some of the plants for your specific location.
Here are some of your local native plants that the City of New York Parks & Recreation suggests for the garden:
Asarum canadense (Canada wild ginger)
Asclepias tuberosa (butterflyweed)
Geranium maculatum (spotted geranium)
Lupinus perennis (sundial lupine)
Monarda punctata (spotted beebalm)
Opuntia humifusa (Devil's tongue)
Phlox subulata (creeping phlox)
Polygonatum biflorum (smooth Solomon’s seal)
Solidago caesia (wreath goldenrod)
Symphyotrichum laeve (smooth blue aster)
Uvularia perfoliata (perfoliate bellwort)
Viola pedata (birdfoot violet)