Disposing of construction debris

To save some money, I am going to be doing the demo for my apt renovation in Manhattan. I am estimating about 5-7 tons of waste, mostly drywall and wood flooring. It looks like curbside pick-up is limited to 6 bags at 60 pounds each, which would take about 2 months to clear out. Any other cost-effective ways to get rid of the waste? Can we get a u-haul and drop off at a local dump? If so, does anyone know what that usually costs?