Assuming everything goes as planned, these will be the skyscrapers with roof heights over 300M in NYC at various stages of completeion, construction and site prep by 2020:
Key:
■ : No work has been done on this building at the time of this post
■ : Site prep, no matter how minimal, has been done at the time of this post
■ : Construction is on hold
■ : The building is under construction
■ : The building has been completed
Grand Central Tower ~500M (Site Prep by 2020)
225 W57th ~450M (Completed by 2020)
432 Park -425M (Completed by 2016)
One World Trade Center -417M (Completed 2013)
Two World Trade Center -411M (Completed by 2020)
Hudson Yards North Office Tower -394M (Completed by 2018)
Empire State Building -381M (Completed 1931)
15 Penn -371M (Site Prep by 2020)
One Manhattan West -371M (Completed by 2020)
Three World Trade Center -327M (Completed by 2018)
Girasole -323M (Completed by 2020) (Possibly +400M)
Tower Verre -320M (Completed by 2018)
Hudson Yards South Office Tower -310M (Completed by 2015)
One57 -306M (Completed 2013)
34th and 10th Street +304M (Site Prep by 2020)
One Hudson Yards +304M (Completed by 2020)
Hudson Yards Mixed-used Tower +304M (U/C by 2020)
237 Park +304M (Site Prep by 2020)
(my list re-posted from Hunser's NY supertalls thread)