EWR makes New York feel possible, and sometimes it is. The better layover may be Newark, Jersey City, or one Manhattan stop near transit rather than a full city wish list.
What to do with bags
If you cannot check the bag through or early, choose a storage-confirmed plan before leaving. A rolling suitcase can make NYC transit stairs and crowds a poor bargain.
Leaving the airport
NJ Transit can put Manhattan within reach on a long layover. For shorter windows, Newark Ironbound or a close hotel/restaurant reset is safer.
Getting back through security
Account for AirTrain time, train schedules, and terminal security. Do not rely on the best-case train connection.