Air from Newark International Airport (EWR); private jets to Teterboro Airport (TEB). Buses from Port Authority Bus Terminal or George Washington Bridge Bus Terminal. Amtrak to Penn Station-New York or Penn Station-Newark.
Rent a car; Hackensack honestly isn't safe enough to wander around any more.
New Jersey Transit buses connect Hackensack to many cities within New Jersey as well as the Port Authority Bus Terminal in midtown Manhattan. Many of the routes originate/terminate or stop at the Hackensack Bus Terminal.
Fare between Hackensack and NY is less than $5. Discounted rates for Seniors/Children.
Check the website for route/schedule/fare information.
To reach Hackensack by train, take New Jersey Transit's Pascack Valley Line. The Pascack Valley Line runs north from Hoboken, New Jersey to Spring Valley, New York. To travel between Manhattan and Hackensack, take the NJ Transit from NY Penn Station to Hoboken (or Secaucus Junction) to pick up the Pascack Valley Line.
There are two stations in Hackensack. Anderson Street Station serves central Hackensack. Essex Street Station serves the southern portions of the city. You can access northern Hackensack (including The Shops at Riverside) by the New Bridge Landing Station in River Edge.
Check the website for schedule information.