There is almost always some ballet being performed in NYC!
You just need to look beyond NYCB and ABT.
The Vail Festival Remix is at City Center this coming week, Thursday through Sunday, though Sunday's performance is more of a demonstration of sorts. Very well known dancers are participating such as Wendy Whelan, Tiler Peck, Robbie Fairchild, Herman Cornejo, Isabella Boylston, Calvin Royale, Carla Korbes, and so many more! You will be able to see dancers from both NYCB and ABT on the same stage plus much more. Check the NYCityCenter.org website for tickets. They can be quite reasonable.
Also, there's dance at the Brooklyn Academy of Music and at the Joyce most weekends as well.